Groups with restrictions on subgroups of infinite rank

被引：27
作者：
De Falco, Maria [1 ]
de Giovanni, Francesco [1 ]
Musella, Carmela [1 ]
Trabelsi, Nadir [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：
REVISTA MATEMATICA IBEROAMERICANA | 2014年 / 30卷 / 02期
关键词：
Prufer rank; strongly locally graded group; quasihamiltonian group; BY-FINITE GROUPS; CONJUGACY CLASSES; PROPER SUBGROUPS; LATTICE;
D O I：
10.4171/RMI/792
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is known that a (generalized) soluble group whose proper subgroups of infinite rank are abelian either is abelian or has finite rank. It is proved here that if G is a group of infinite rank such that all its proper subgroups of infinite rank have locally finite commutator subgroup, then the commutator subgroup G' of G is locally finite, provided that G satisfies a suitable generalized solubility condition. Moreover, a similar result is obtained for groups whose proper subgroups of infinite rank are quasihamiltonian.
引用
收藏
页码：537 / 550
页数：14
相关论文
共 22 条
[1]  
BELYAEV VV, 1975, ACTA MATH ACAD SCI H, V26, P369
[2]  
CERNIKOV NS, 1990, UKR MATH J, V42, P855
[3]   GROUPS WHOSE PROPER SUBGROUPS OF INFINITE RANK HAVE FINITE CONJUGACY CLASSES [J].
De Falco, M. ;
De Giovanni, F. ;
Musella, C. ;
Trabelsi, N. .
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2014, 89 (01) :41-48
[4]   Periodic groups with nearly modular subgroup lattice [J].
De Falco, M ;
De Giovanni, F ;
Musella, C ;
Sysak, YP .
ILLINOIS JOURNAL OF MATHEMATICS, 2003, 47 (1-2) :189-205
[5]   GROUPS WHOSE FINITE HOMOMORPHIC IMAGES ARE METAHAMILTONIAN [J].
De Falco, Maria ;
De Giovanni, Francesco ;
Musella, Carmela .
COMMUNICATIONS IN ALGEBRA, 2009, 37 (07) :2468-2476
[6]   Groups with almost modular subgroup lattice [J].
de Giovanni, F ;
Musella, C ;
Sysak, YP .
JOURNAL OF ALGEBRA, 2001, 243 (02) :738-764
[7]   Groups with all subgroups permutable or of finite rank [J].
Dixon, Martyn R. ;
Karatas, Yalcin .
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2012, 10 (03) :950-957
[8]   Locally (soluble-by-finite) groups of finite rank [J].
Dixon, MR ;
Evans, MJ ;
Smith, H .
JOURNAL OF ALGEBRA, 1996, 182 (03) :756-769
[9]   Groups with all proper subgroups (finite rank)-by-nilpotent [J].
Dixon, MR ;
Evans, MJ ;
Smith, H .
ARCHIV DER MATHEMATIK, 1999, 72 (05) :321-327
[10]   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
123