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Certain combinatorial topics in group theory | ||
| International Journal of Group Theory | ||
| مقاله 8، دوره 2، شماره 1، خرداد 2013، صفحه 91-107 اصل مقاله (495.11 K) | ||
| نوع مقاله: Ischia Group Theory 2012 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2439 | ||
| نویسنده | ||
| C. Gupta* | ||
| University of Manitoba | ||
| چکیده | ||
| This article is intended to be a survey on some combinatorial topics in group theory. The bibliography at the end is neither claimed to be exhaustive, nor is it necessarily connected with a reference in the text. I include it as I see it revolves around the concepts which are discussed in the text. | ||
| کلیدواژهها | ||
| automorphisms؛ test words؛ polynilpotent series؛ universal theories | ||
| مراجع | ||
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K.~S.~Allambergenov and V.~A.~Roman'kov (1984) Products of commutators in groups Dokl. Akad. Nauk UzSSR 4, 14-15
S.~Bachmuth (1966) Induced automorphisms of free groups and free metabelian groups Trans. Amer. Math. Soc. 122, 1-17
S.~Bachmuth (1965) Automorphisms of free metabelian groups Trans. Amer. Math. Soc. 118, 93-104
S.~Bachmuth, E.~Formanek and H.~Y.~Mochizuki (1967) $\IA$-automorphisms of certain two generator torsion-free groups J.~Algebra 40, 19-30
G.~Baumslag, A.~Myasnikov and V.~Remeslennikov (2000) Algebraic geometry over groups Trends Math., Birkhauser, Boston , 35-50
G.~Baumslag, A.~Myasnikov and V.~Remeslennikov (1999) Algebraic geometry over groups. I. Algebraic sets and ideal theory J.~Algebra 219 (1), 16-79
G.~Baumslag, A.~Myasnikov and V.~Roman'kov (1997) Two theorems about equationally noetherian groups J.~Algebra 194 (2), 654-664
J. S.~Birman (1973) An inverse function theorem for free groups Proc. Amer. Math. Soc. 41, 634-638
R.~Bryant (1977) The verbal topology of a group J.~Algebra 48, 340-346
R.~M.~Bryant and J.~R.~J.~Groves (1992) Automorphisms of free metabelian groups of infinite rank Comm. Algebra 20, 783-814
R.~M.~Bryant and C.~K.~Gupta (1993) Automorphisms of free nilpotent-by-abelian groups Math. Proc. Cambridge Philos. Soc. 114, 143-147
R.~M.~Bryant and C.~K.~Gupta (1989) Automorphism groups of free nilpotent groups Arch. Math. (Basel) 52, 313-320
R.~M.~Bryant and Olga Macedonska (1989) Automorphisms of relatively free nilpotent groups of infinite rank J.~Algebra 121, 388-398
R.~M.~Bryant and V.~A.~Roman'kov (1999) Automorphisms groups of relatively free groups Math. Proc. Cambridge Philos. Soc. 127 (3), 411-424
R.~G.~Burns and L.~Pi (1989) Generators for the bounded automorphisms of infinite-rank free nilpotent groups Bull. Austral. Math. Soc. 40 (2), 175-187
O.~Chapuis (1995) Universal theory of certain solvable groups and bounded Ore group rings J.~Algebra 176 (2), 368-391
I.~V.~Chirkov and M.~A.~Shevelin (2002) Test sets in free metabelian Lie algebras Sibirsk. Mat. Zh. 43 (6), 1401-1407
D. E.~Cohen (1978) Combinatorial group theory. A topological approach Queen Mary College Mathematical Notes, Queen Mary College, Department of Pure Mathematics, London
R.~H.~Crowell and R.~H.~Fox (1963) Introduction to knot theory Ginn, Boston, MA
A. Dold (1988) Nullhomologous words in free groups which are not nullhomologous in any proper subgroup Arch. Math. (Basel) 50 (6), 564-569
A.~J.~Duncan, I.~V.~Kazachkov and V.~N.~Remeslennikov (2007) Parabolic and quasiparabolic subgroups of free partially commutative groups J.~Algebra 318 (2), 918-932
A.~J.~Duncan, I.~V.~Kazachkov and V.~N.~Remeslennikov (2006) Centraliser dimension of partially commutative groups Geom. Dedicata 120, 73-97
V.~G.~Durnev (1989) The Mal'tsev--Nielsen equation on a free metabelian group of rank~$2$ Mat. Zametki 46, 57-60
V.~I.~Epanchintsev and G.~P.~Kukin (1979) The word problem in a variety of groups that contain ${\frak N}\sb{2}{\frak A}$ Algebra i Logika 18 (3), 259-285
B.~Fine, G.~Rosenberger, D.~Spellman and M.~Stille (1999) Test words, generic elements and almost primitivity Pacific J. Math. 190 (2), 277-297
E. Formanek and C. Procesi (1992) The automorphism group of a free group is not linear J.~Algebra 149, 494-499
R.~H.~Fox (1953) Free differential calculus I. Derivations in the free group ring Ann. of Math. (2) 57, 547-560
R.~I.~Grigorchuk and P.~F.~Kurchanko (1993) Certain questions of group theory related to geometry Encyclopaedia of Mathematical Sciences, Algebra~VII, Combinatorial Group Theory, Applications to Geometry, Springer , 173-231
C.~K.~Gupta (1973) The free centre-by-metabelian groups J. Austral. Math. Soc. 16, 294-299
C.~K.~Gupta and N.~D.~Gupta (1992) Lifting primitivity of free nilpotent groups Proc. Amer. Math. Soc. 114, 617-621
C.~K.~Gupta, N.~D.~Gupta and F.~Levin (1987) On dimension subgroups relative to certain product ideals Lecture Notes in Math. 1281, 31-35
C.~K.~Gupta, N.~D.~Gupta and G.~A.~Noskov (1994) Some applications of Artamonov--Quillen--Suslin theorems to metabelian inner-rank and primitivity Canad. J. Math. 46, 298-307
C.~K.~Gupta, N.~D.~Gupta and A.~S.~Oliynyk (2007) Free products of finite groups acting on regular rooted trees Algebra Discrete Math. 2007 (2), 91-103
C.~K.~Gupta, N.~D.~Gupta and V.~A.~Roman'kov (1992) Primitivity in free groups and free metabelian groups Canad.\ J.\ Math. 44, 516-523
C.~K.~Gupta and W.~Holubowski (2008) Automorphisms of a free group of infinite rank St.~Petersburg Math.~J. 19 (2), 215-223
C.~K.~Gupta, V.~A.~Roman'kov and E.~I.~Timoshenko (2005) Test ranks of free nilpotent groups Comm. Algebra 33, 1627-1634
C.~K.~Gupta and N.~S.~Romanovskii (2007) The property of being equational Noetherian of some solvable groups Algebra Logic 46 (1), 28-36
C.~K.~Gupta and N.~S.~Romanovskii (2006) The word problem for polynilpotent groups with a single primitive defining relation Algebra Logic 45 (1), 17-25
C.~K.~Gupta and N.~S.~Romanovskii (2004) On torsion in factors of polynilpotent series of a group with a single relation Internat. J. Algebra Comput. 14 (4), 513-523
C.~K.~Gupta and E.~I.~Timoshenko (2012) Properties and universal theories for partially commutative nilpotent metabelian groups Algebra Logic 51 (4), 285-305
C.~K.~Gupta and E.~I.~Timoshenko (2011) On Universal theories for partially commutative metabelian groups Algebra Logic 50 (1), 1-16
C.~K.~Gupta and E.~I.~Timoshenko (2009) Partially commutative metabelian groups, Centralizers and elementary equivalence Algebra Logika 48 (3), 309-341
C.~K.~Gupta and E.~I.~Timoshenko (2008) Test rank of the solvable product of free abelian groups Sb. Math. 199 (4), 495-510
C.~K.~Gupta and E.~I.~Timoshenko (2004) A criterion for invertibility of endomorphisms and the test rank of metabelian products of abelian groups Algebra Logic 43 (5), 316-326
C.~K.~Gupta and E.~I.~Timoshenko (2003) Test Rank for Some Free Polynilpotent Groups Algebra Logic 42 (1), 20-28
C.~K.~Gupta and E.~I.~Timoshenko (2001) Generating elements for groups of the form $F/R'$ Algebra Logic 40 (3), 137-143
N.~Gupta (1987) Free group rings Contemporary Mathematics, American Mathematical Society, Providence, RI 66
N.~Gupta and V.~Shpilrain (1993) Nielsen's commutator test for two-generator groups Math. Proc. Cambridge Philos. Soc. 114 (2), 295-301
W.~Imrich and E.~C.~Turner (1989) Endomorphisms of free groups and their fixed points Math. Proc. Cambridge Philos. Soc. 105, 421-422
W.~Jaco (1969) Heegaard splittings and splitting homomorphisms Trans. Amer. Math. Soc. 144, 365-379
A.~Karrass, W.~Magnus and D.~Solitar (1960) Elements of finite order in groups with a single defining relation Comm. Pure Appl. Math. 13, 57-66
O.~G.~Kharlampovich (1986) Algorithmic problems for subvarieties of $\frakN_2 \fraka$ Proc. 8th All-Union Conf. Math. Logic, Moscow , 197
O.~G.~Kharlampovich (1981) A Finitely presented solvable group with undecidable word problem Izv.\ Akad.\ Nauk SSSR Ser.\ Mat. 45 (4), 852-873
A.~F.~Krasnikov (1978) Generators of the group $F/[N,N]$ Mat. Zametki 24, 167-173
P.~H.~Kropholler, P.~A.~Linnell and J.~A.~Moody (1988) Applications of a new $K$-theoretic theorem to soluble group rings Proc. Amer. Math. Soc. 104 (3), 675-684
R.~C.~Lyndon and P.~E.~Schupp (1977) Combinatorial group theory Erbeg. Math. Grenzgeb.,
Springer-Verlag, Berlin 89
W.~Magnus (1934) \"Uber $n$-dimensionale Gittertransformationen Acta Math. 64, 353-367
W.~Magnus, A.~Karrass and D.~Solitar (1966) Combinatorial Group Theory Intersicence Publ., New York
W.~Magnus and C.~Tretkoff (1980) Representations of automorphism groups of free groups Word Problems II, Studies in Logic and Foundations of Mathematics, North Holland, Oxford 95, 255-260
A.~I.~Mal'tsev (1955) Two remarks on nilpotent groups Mat. Sb. (N.S.) 37 (79), 567-572
A.~I.~Mal'tsev (1948) Embeddings of group algebras in division algebras Dokl. Akad. Nauk SSSR 60 (9), 1499-1501
V.~D.~Mazurov and E.~I.~Khukhro (eds.) (2002) Kourovka Notebook. Unsolved problems in group theory 15th edition, Institute of Mathematics, SO RAN, Novosibirsk
J.~McCool (1974) A Presentation for the Automorphism Group of a Free Group of Finite Rank J.~London Math.\ Soc. 8 (2), 259-266
A.~A.~Mishchenko and E.~I.~Timoshenko (2011) Universal equivalence of partially commutative nilpotent groups Sibirsk. Mat. Zh. 52 (5), 1113-1122
A.~Myasnikov and V.~N.~Remeslennikov (2000) Algebraic geometry over groups. II. Logical foundations J.~Algebra 234 (1), 225-276
B.~H.~Neumann (1967) Varieties of groups Springer, New York
B.~H.~Neumann (1933) Die Automorphismengruppe der freien Gruppen Math. Ann. 107, 367-386
J.~Nielsen (1924) Die Isomorphismengruppe der freien Gruppen Math. Ann. 91, 169-209
J.~Nielsen (1918) \"Uber die Isomorphismen unendlicher Gruppe ohne Relation Math. Ann. 79, 269-272
J.~Nielsen (1917) Die Isomorphismen der allgemeinen, unendlichen Gruppe mit zwei Erzeugenden Math. Ann. 78, 385-397
E.~S.~Rapaport (1958) On free groups and their automorphisms Acta Math. 99, 139-163
V.~N.~Remeslennikov (1973) Example of a finitely presented group in the variety $\fraka^5$ with undecidable word problem Algebra Logika 12 (5), 577-602
V.~N.~Remeslennikov and N.~S.~Romanovskii (2004) Metabelian products of groups Algebra i Logika 43 (3), 341-352
V.~N.~Remeslennikov and V.~G.~Sokolov (1970) Certain properties of the Magnus embedding Algebra i Logika 9, 566-578
V.~N.~Remeslennikov and A.~V.~Treier (2010) The Structure of the automorphism group for partially commutative class two nilpotent groups Algebra i Logika 49 (1), 60-97
A.~H.~Rhemtulla (1969) Commutators of certain finitely generated soluble groups Canad. J. Math. 21 (5), 1160-1164
I.~A.~Rips (1969) On certain classes of groups of the type of groups with a category Ural. Gos. Univ. Mat. Zap. 7 (3), 183-194
V.~A.~Roman'kov (2001) On test elements of free solvable groups of rank~2 Algebra i Logika 40, 192-201
V.~A.~Roman'kov (1992) Automorphisms of groups Acta Appl. Math. 29, 241-280
V.~A.~Roman'kov (1992) Generators for the automorphism groups of free metabelian pro-$p$-groups Sibirsk. Mat. Zh. 33 (5), 878-890
V.~A.~Roman'kov (1985) The automorphism groups of free metabelian groups Proc.\ Comupter Centre, USSR Academy of Sciences, Novosibirsk , 35-81
V.~A.~Roman'kov (1982) Width of verbal subgroups of solvable groups Algebra i Logika 21 (1), 60-72
N.~S.~Romanovskii (1999) A Freiheitssatz for products of groups Algebra i Logika 38 (3), 354-367
N.~S.~Romanovskii (1974) On some algorithmic problems for solvable groups Algebra Logic 13, 26-34
G.~Rosenberger (1984) \"Uber Darstellungen von Elementen und Untergruppen in freien Produkten Proc.\ Conf.\ Combinatorial Group Theory (Groups--Korea 1983, Kyoungju, Korea, 1983, Lecture Notes in Math. 1098, 142-160
A.~L.~Shmel'kin (1969) On free products of groups Mat. Sb. 79 (4), 616-620
A.~L.~Shmel'kin (1967) Two remarks on free solvable groups Algebra i Logika 6 (2), 95-109
V.~Shpilrain (1995) On monomorphisms of free groups Arch. Math. (Basel) 64, 465-470
V.~Shpilrain (1995) Test elements for endomorphisms of free groups and algebras Israel J. Math. 92, 307-316
V.~Shpilrain (1994) Recognizing automorphisms of the free groups Arch. Math. (Basel) 62 (5), 385-392
V.~Shpilrain (1991) Automorphisms of $F/R'$ groups Internat. J. Algebra Comput. 1, 177-184
E.~I.~Timoshenko (2011) A Mal'tsev basis for a partially commutative nilpotent metabelian group Algebra Logika 50 (5), 647-658
E.~I.~Timoshenko (2010) Universal equivalence of partially commutative metabelian groups Algebra Logika 49 (2), 263-290
E.~I.~Timoshenko (2001) On Universal theories of metabelian groups and the Shmel'kin embedding Sibirsk. Mat. Zh. 42 (5), 1168-1175
E.~I.~Timoshenko (2000) Test elements and test ranks of a free metabelian groups Sibirsk. Mat. Zh. 41 (6), 1451-1456
E.~I.~Timoshenko (1973) Algorithmic problems for metabelian groups Algebra Logic 12, 132-137
E.~Turner (1996) Test words for automorphisms of free groups Bull. London Math. Soc. 28 (3), 255-263
J.~H.~C.~Whitehead (1936) On certain sets of elements in a free group Proc. London Math. Soc. 41, 48-56
J.~H.~C.~Whitehead (1936) On equivalent sets of elements in a free group Ann. of Math. (2) 37, 782-800
C.~Wrathall (1989) Free partially commutative groups ombinatorics, Computing, Complexity (Tianjing and Beijing, 1988),
Math. Appl. (Chinese Ser.), Kluwer Acad. Publ., Dordrecht 1
H.~Zieschang (1966) \"Uber Automorphismen ebener diskontinuierlicher Gruppen Math. Ann. 166 (2), 148-167
H.~Zieschang (1964) Alternierende Produkte in freien Gruppen Abh. Math. Sem. Univ. Hamburg 27, 13-31
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