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de Giovanni, Francesco, Trombetti, Marco. (1392). Groups with minimax commutator subgroup. , 3(1), 9-16. doi: 10.22108/ijgt.2014.2968
Francesco de Giovanni; Marco Trombetti. "Groups with minimax commutator subgroup". , 3, 1, 1392, 9-16. doi: 10.22108/ijgt.2014.2968
de Giovanni, Francesco, Trombetti, Marco. (1392). 'Groups with minimax commutator subgroup', , 3(1), pp. 9-16. doi: 10.22108/ijgt.2014.2968
de Giovanni, Francesco, Trombetti, Marco. Groups with minimax commutator subgroup. , 1392; 3(1): 9-16. doi: 10.22108/ijgt.2014.2968

Groups with minimax commutator subgroup

International Journal of Group Theory
مقاله 2، دوره 3، شماره 1، خرداد 2014، صفحه 9-16    اصل مقاله (272.57 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2014.2968
نویسندگان
Francesco de Giovanni* 1؛ Marco Trombetti2
1Dipartimento di Matematica e Applicazioni - University of Napoli "Federico II"
2Dipartimento di Matematica e Applicazooni - University of Napoli "Federico II"
چکیده
A result of Dixon‎, ‎Evans and Smith shows that if $G$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $G$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $G$ has finite rank‎. ‎It is proved here that if $G$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator subgroup $G'$ of $G$ is minimax‎. ‎A corresponding result is proved for groups in which the commutator subgroup of every proper subgroup has finite torsion-free rank.‎
کلیدواژه‌ها
minimax group؛ commutator subgroup؛ torsion-free rank
مراجع
V. V. Belyaev and N. F. Sesekin (1975) On infinite groups of Miller-Moreno type Acta Math. Acad. Sci. Hungar. 26, 369-376
N. S. Cernikov (1990) Theorem on groups of finite special rank Ukrain. Math. J. 24, 855-861
M. De Falco, F. de Giovanni, C. Musella and N. Trabelsi Groups with restrictions on subgroups of infinite rank Rev. Mat. Iberoamericana, to appear
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
M. R. Dixon and Z. Y. Karatas (2012) Groups with all subgroups permutable or of finite rank Centr. Eur. J. Math. 10, 950-957
S. Franciosi, F. de Giovanni and M. J. Tomkinson (1991) Groups with Cernikov conjugacy classes J. Austral. Math. Soc. Ser. A 50, 1-14
F. de Giovanni and M. Trombetti Groups whose proper subgroups of infinite rank have polycyclic conjugacy classes Algebra Colloq., to appear
J. Otal and J. M. Pena (1988) Minimal non-CC-groups Comm. Algebra 16, 1231-1242
Y. D. Polovickii (1964) Groups with extremal classes of conjugate elements Sibirskii Mat. Z. 5, 891-895
D. J. S. Robinson (1972) Finiteness conditions and generalized soluble groups Springer, Berlin
O. A. Yarovaya (2008) On groups whose all proper subgroups are close to abelian ones Visn. Kyiv Univ. Ser. Fiz--Mat. Nauk 4, 36-39
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