GROUPS WHOSE PROPER SUBGROUPS OF INFINITE RANK HAVE FINITE CONJUGACY CLASSES

被引：20
作者：
De Falco, M. [1 ]
De Giovanni, F. [1 ]
Musella, C. [1 ]
Trabelsi, N. [2 ]
机构：
[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz, I-80126 Naples, Italy
[2] Univ Setif, Dept Math, Lab Fundamental & Numer Math, Setif 19000, Algeria
来源：
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2014年 / 89卷 / 01期
关键词：
finite rank; FC-group;
D O I：
10.1017/S0004972713000014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A group G is said to be an FC-group if each element of G has only finitely many conjugates, and G is minimal nonFC if all its proper subgroups have the property FC but G is not an FC-group. It is an open question whether there exists a group of infinite rank which is minimal nonFC. We consider here groups of infinite rank in which all proper subgroups of infinite rank are FC, and prove that in most cases such groups are either FC-groups or minimal nonFC.
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页码：41 / 48
页数：8
相关论文
共 15 条
[1]  
Amberg B., 1992, Products of Groups
[2]  
BELYAEV VV, 1975, ACTA MATH ACAD SCI H, V26, P369
[3]  
BELYAEV VV, 1980, P ALL UN S GROUP THE, P97
[4]  
CERNIKOV NS, 1990, UKR MATH J, V42, P855
[5]  
De Falco M., REV MAT IBE IN PRESS
[6]   Locally (soluble-by-finite) groups of finite rank [J].
Dixon, MR ;
Evans, MJ ;
Smith, H .
JOURNAL OF ALGEBRA, 1996, 182 (03) :756-769
[7]   Groups with all proper subgroups (finite rank)-by-nilpotent [J].
Dixon, MR ;
Evans, MJ ;
Smith, H .
ARCHIV DER MATHEMATIK, 1999, 72 (05) :321-327
[8]   Locally (soluble-by-finite) groups with all proper non-nilpotent subgroups of finite rank [J].
Dixon, MR ;
Evans, MJ ;
Smith, H .
JOURNAL OF PURE AND APPLIED ALGEBRA, 1999, 135 (01) :33-43
[9]   Groups with many FC-subgroups [J].
Franciosi, S ;
de Giovanni, F ;
Sysak, YP .
JOURNAL OF ALGEBRA, 1999, 218 (01) :165-182
[10]   A CHARACTERIZATION OF SOME LOCALLY FINITE SIMPLE-GROUPS OF LIE TYPE [J].
KLEIDMAN, PB ;
WILSON, RA .
ARCHIV DER MATHEMATIK, 1987, 48 (01) :10-14
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