تعداد نشریات | 43 |
تعداد شمارهها | 1,682 |
تعداد مقالات | 13,758 |
تعداد مشاهده مقاله | 32,155,692 |
تعداد دریافت فایل اصل مقاله | 12,731,324 |
The prime graph conjecture for integral group rings of some alternating groups | ||
International Journal of Group Theory | ||
مقاله 15، دوره 2، شماره 1، خرداد 2013، صفحه 175-185 اصل مقاله (438.38 K) | ||
نوع مقاله: Ischia Group Theory 2012 | ||
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2759 | ||
نویسنده | ||
Mohamed Salim* | ||
UNITED ARAB EMIRATES UNIVERSITY | ||
چکیده | ||
We investigate the classical H. Zassenhaus conjecture for integral group rings of alternating groups $A_9$ and $A_{10}$ of degree $9$ and $10$, respectively. As a consequence of our previous results we confirm the Prime Graph Conjecture for integral group rings of $A_n$ for all $n \leq 10$. | ||
کلیدواژهها | ||
integral group ring؛ Zassenhaus Conjecture؛ Prime Graph Conjecture؛ torsion unit | ||
مراجع | ||
V.~A. Artamonov and A.~A. Bovdi (1991) Integral group rings: groups of invertible elements and classical
{$K$}-theory Algebra. {T}opology. {G}eometry, Vol. 27 ({R}ussian), Itogi Nauki i Tekhniki, 3--43, 232, Akad. Nauk SSSR Vsesoyuz. Inst.
Nauchn. i Tekhn. Inform., Moscow, 1989.
Translated in J. Soviet Math. 57 (2), 2931-2958
V.~Bovdi, A.~Grishkov and A.~Konovalov (2009) Kimmerle conjecture for the {H}eld and {O}'{N}an sporadic simple
groups Sci. Math. Jpn. 69 (3), 353-361
V. Bovdi and M.~Hertweck (2008) Zassenhaus conjecture for central extensions of ${S}_{5}$ J. Group Theory 11 (1), 63-74
V.~Bovdi, C.~H{\"o}fert and W.~Kimmerle (2004) On the first {Z}assenhaus conjecture for integral group rings Publ. Math. Debrecen 65 (3-4), 291-303
V.~Bovdi and A.~Konovalov (2007) Integral group ring of the first {M}athieu simple group In Groups St. Andrews 2005. Vol. 1, volume 339 of London
Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge , 237-245
V.~Bovdi and A.~Konovalov (2008) Integral group ring of the {M}athieu simple group {$M\sb{23}$} Comm. Algebra 36 (7), 2670-2680
V.~Bovdi and A.~Konovalov (2009) Integral group ring of {R}udvalis simple group Ukra\"\i n. Mat. Zh. 61 (1), 3-13
V.~Bovdi and A.~Konovalov (2012) Integral group ring of the {M}athieu simple group {$M_{24}$} J. Algebra Appl., 1250016, 10pp 11 (1)
V.~Bovdi and A.~Konovalov (2010) Torsion units in integral group ring of {H}igman-{S}ims simple group Studia Sci. Math. Hungar. 47 (1), 1-11
V.~Bovdi, A.~Konovalov and S.~Linton (2008) Torsion units in integral group ring of the {M}athieu simple group ${\rm M}\sb {22}$ LMS J. Comput. Math. 11, 28-39
V.~Bovdi, A.~Konovalov and E.~Marcos (2008) Integral group ring of the {S}uzuki sporadic simple group Publ. Math. Debrecen 72 (3-4), 487-503
V.~Bovdi, A.~Konovalov, and S.~Siciliano (2007) Integral group ring of the {M}athieu simple group {$M\sb{12}$} Rend. Circ. Mat. Palermo (2) 59 (1), 125-136
V.~A. Bovdi, E.~Jespers and A.~B. Konovalov (2011) Torsion units in integral group rings of {J}anko simple groups Math. Comp. 80 (273), 593-615
V.~A. Bovdi and A.~B. Konovalov, (2007) Integral group ring of the {M}c{L}aughlin simple group Algebra Discrete Math. 2, 43-53
V.~A. Bovdi, A.~B. Konovalov and S.~Linton (2011) Torsion units in integral group rings of {C}onway simple groups Internat. J. Algebra Comput. 21 (4), 615-634
M.~Caicedo, L.~Margolis and {\'A}.~del R{\'{\i}}o (2012) Zassenhaus conjecture for cyclic-by-abelian groups to appear in Journal of the London Mathematical Society , 1-15
J.~Cohn and D.~Livingstone (1965) On the structure of group algebras. {I} Canad. J. Math. 17, 583-593
GAP -- Groups, Algorithms, and Programming, Version 4.4.12 (2008) \href{http://www.gap-system.org}{http://www.gap-system.org}
J.~Gildea (2013) Zassenhaus conjecture for integral group ring of simple linear
groups to appear J. Algebra Appl. , 1-13
M.~Hertweck (2006) On the torsion units of some integral group rings Algebra Colloq. 13 (2), 329-348
M.~Hertweck (2008) Zassenhaus conjecture for {$A_6$} Proc. Indian Acad. Sci. Math. Sci. 118 (2), 189-195
M.~Hertweck (2007) Partial augmentations and {B}rauer character values of torsion units in group rings to appear in Comm. Algebra, (E-print \verb+arXiv:math.RA/0612429v2+) , 1-16
W.~Kimmerle (2006) On the prime graph of the unit group of integral group rings of
finite groups In Groups, rings and algebras, volume 420 of Contemp.
Math., pages 215--228. Amer. Math. Soc., Providence, RI
I.~S. Luthar and I.~B.~S. Passi (1989) Zassenhaus conjecture for {$A\sb 5$} Proc. Indian Acad. Sci. Math. Sci. 99 (1), 1-5
Mini-{W}orkshop: {A}rithmetik von {G}ruppenringen (2007) Abstracts from the mini-workshop held November 25–December 1, 2007, Organized by Eric Jespers, Zbigniew Marciniak, Gabriele Nebe and Wolfgang Kimmerle. Oberwolfach Reports, Vol. 4 no. 4, Oberwolfach Rep. 4 (4), 3209-3239
K.~Roggenkamp and L.~Scott (1987) Isomorphisms of {$p$}-adic group rings Ann. of Math. (2) 126 (3), 593-647
M.~A.~M. Salim (2007) Torsion units in the integral group ring of the alternating group of degree 6 Comm. Algebra 35 (12), 4198-4204
M.~A.~M. Salim (2011) Kimmerle's conjecture for integral group rings of some alternating
groups Acta Math. Acad. Paedagog. Nyh\'azi. (N.S.) 27 (1), 9-22
A.~Weiss (1991) Torsion units in integral group rings J. Reine Angew. Math. 415, 175-187
H.~Zassenhaus (1974) On the torsion units of finite group rings In Studies in mathematics (in honor of A. Almeida Costa)
(Portuguese), Instituto de Alta Cultura, Lisbon , 119-126
| ||
آمار تعداد مشاهده مقاله: 4,657 تعداد دریافت فایل اصل مقاله: 3,249 |