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Metahamiltonian groups and related topics | ||
International Journal of Group Theory | ||
مقاله 10، دوره 2، شماره 1، خرداد 2013، صفحه 117-129 اصل مقاله (423.39 K) | ||
نوع مقاله: Ischia Group Theory 2012 | ||
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2673 | ||
نویسندگان | ||
Maria De Falco1؛ Francesco de Giovanni* 2؛ Carmela Musella1 | ||
1Dipartimento di Matematica e Applicazioni - University of Napoli "Federico II" | ||
2Dipartimento di Matematica e Applicazioni - University of Napoli "Federico II" | ||
چکیده | ||
A group $G$ is called metahamiltonian if all its non-abelian subgroups are normal. The aim of this paper is to provide an updated survey of research concerning certain classes of generalized metahamiltonian groups, in various contexts, and to prove some new results. Some open problems are listed. | ||
کلیدواژهها | ||
Metahamiltonian group؛ normalizer subgroup؛ lattice property | ||
مراجع | ||
B. Amberg, S. Franciosi and F. de Giovanni (1992) Products of groups Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York
B. Bruno and R. E. Phillips (1981) Groups with restricted non-normal subgroups Math. Z. 176 (2), 199-221
M. R. Celentani and U. Dardano (1993) Groups whose infinite proper subgroups are $T$-groups Note Mat. 13 (2), 295-307
S. N. \v Cernikov (1971) Infinite nonabelian groups in which all infinite nonabelian subgroups are invariant Ukrain. Math. J. 23, 498-517
M. De Falco, F. de Giovanni and C. Musella (2007) Groups whose non-normal subgroups have small commutator subgroup Algebra Discrete Math. (3), 46-58
M. De Falco, F. de Giovanni and C. Musella (2008) The Schur property for subgroup lattices of groups Arch. Math. (Basel) 91 (2), 97-105
M. De Falco, F. de Giovanni and C. Musella (2009) Groups whose finite homomorphic images are metahamiltonian Comm. Algebra 37 (7), 2468-2476
M. De Falco, F. de Giovanni and C. Musella On a class of metahamiltonian groups Ricerche Mat., to appear.
M. De Falco, F. de Giovanni, C. Musella and R. Schmidt (2003) Groups in which every non-abelian subgroup is permutable Rend. Circ. Mat. Palermo (2) 52 (1), 70-76
M. De Falco, F. de Giovanni, C. Musella and R. Schmidt (2003) Groups with metamodular subgroup lattice Colloq. Math. 95 (2), 231-240
M. De Falco, F. de Giovanni, C. Musella and Y. P. Sysak (2003) Periodic groups with nearly modular subgroup lattice Illinois J. Math. 47 (1-2), 189-205
M. De Falco, F. de Giovanni, C. Musella and Y. P. Sysak (2007) Groups with normality conditions for non-abelian subgroups J. Algebra 315 (2), 665-682
M. De Falco, F. de Giovanni, C. Musella and Y. P. Sysak On metahamiltonian groups of infinite rank to appear.
M. De Falco, F. de Giovanni, C. Musella and N. Trabelsi Groups with restrictions on subgroups of infinite rank Rev. Mat. Iberoam., to appear.
F. De Mari and F. de Giovanni (2005) Groups with few normalizer subgroups Irish Math. Soc. Bull. 56, 103-113
F. De Mari and F. de Giovanni (2006) Groups with finitely many normalizers of non-abelian subgroups Ric. Mat. 55 (2), 311-317
M. R. Dixon, M. J. Evans and H. Smith (1999) Groups with all proper subgroups (finite rank)-by-nilpotent Arch. Math. (Basel) 72, 321-327
I. I. Eremin (1959) Groups with finite classes of conjugate abelian subgroups Mat. Sb. (N.S.) 47, 45-54
M. J. Evans and Y. Kim (2004) On groups in which every subgroup of infinite rank is subnormal of bounded defect Comm. Algebra 32, 2547-2557
F. de Giovanni, C. Musella and Y. P. Sysak (2001) Groups with almost modular subgroup lattice J. Algebra 243 (2), 738-764
L. A. Kurdachenko, J. Otal, A. Russo and G. Vincenzi (2004) Groups whose non-normal subgroups have finite conjugacy classes Math. Proc. R. Ir. Acad. 104A (2), 177-189
L. A. Kurdachenko, J. Otal and I. Subbotin (2002) Groups with prescribed quotient groups and associate module theory World Scientific, Singapore
N. F. Kuzennyi, S. S. Levishchenko and N. N. Semko (1988) Groups with invariant infinite non-abelian subgroups Ukrain. Math. J. 40 (3), 267-273
N. F. Kuzennyi and N. N. Semko (1983) Structure of solvable nonnilpotent metahamiltonian groups Math. Notes 34 (2), 572-577
N. F. Kuzennyi and N. N. Semko (1984) On the structure of infinite nilpotent periodic metahamiltonian groups in Structure of groups and their subgroup characterization, Kiev , 101-111
N. F. Kuzennyi and N. N. Semko (1985) Structure of solvable metahamiltonian groups Dokl. Akad. Nauk Ukrain. SSR Ser. A (2), 6-9
N. F. Kuzennyi and N. N. Semko (1986) On the structure of nonperiodic metahamiltonian groups Izv. Vuzov Matematika 11, 32-38
N. F. Kuzennyi and N. N. Semko (1987) Structure of periodic metabelian metahamiltonian groups with a nonelementary commutator subgroup Ukrain. Math. J. 39 (2), 149-153
N. F. Kuzennyi and N. N. Semko (1988) The structure of periodic metabelian metahamiltonian groups with an elementary commutator subgroup of rank two Ukrain. Math. J. 40 (6), 627-633
N. F. Kuzennyi and N. N. Semko (1989) Structure of periodic nonabelian metahamiltonian groups with an elementary commutator subgroup of rank three Ukrain. Math. J. 41 (2), 153-158
N. F. Kuzennyi and N. N. Semko (1990) Metahamiltonian groups with elementary commutator subgroup of rank two Ukrain. Math. J. 42 (2), 149-154
J. C. Lennox (1973) Finite Frattini factors in finitely generated soluble groups Proc. Amer. Math. Soc. 41, 356-360
A. A. Mahnev (1976) On finite metahamiltonian groups Ural. Gos. Univ. Mat. Zap. 10 (1), 60-75
B. H. Neumann (1955) Groups with finite classes of conjugate subgroups Math. Z. 63, 76-96
R. E. Phillips and J. S. Wilson (1978) On certain minimal conditions for infinite groups J. Algebra 51 (1), 41-68
Y. D. Polovicki\u{\i} (1980) Groups with finite classes of conjugate infinite abelian subgroups Soviet Math. (Iz. VUZ) 24, 52-59
D. J. S. Robinson (1968) Residual properties of some classes of infinite soluble groups Proc. London Math. Soc. (3) 18, 495-520
D. J. S. Robinson (1972) Finiteness conditions and generalized soluble groups Springer, Berlin
G. M. Romalis and N. F. Sesekin (1966) Metahamiltonian groups Ural. Gos. Univ. Mat. Zap. 5, 101-106
G. M. Romalis and N. F. Sesekin (1968) Metahamiltonian groups II Ural. Gos. Univ. Mat. Zap. 6, 52-58
G. M. Romalis and N. F. Sesekin (1969/70) Metahamiltonian groups III Ural. Gos. Univ. Mat. Zap. 7, 195-199
R. Schmidt (1994) Subgroup lattices of groups de Gruyter, Berlin
N. N. Semko and O. A. Yarovaya (2009) On some generalization of metahamiltonian groups Algebra Discrete Math. (2), 70-78
G. Zacher (1980) Una caratterizzazione reticolare della finitezza dell'indice di un sottogruppo in un gruppo Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 69 (6), 317-323
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