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Zbl 0684.20026
Otal, Javier; Peña, Juan Manuel
Groups with minimal conditions related to finiteness properties on conjugacy classes. (English)
[J] Rend. Semin. Mat. Univ. Padova 81, 79-84 (1989). ISSN 0041-8994

This paper is concerned with conditions related to a group being a minimal non-FC-group. The authors have shown previously that a locally graded group in which every proper subgroup is Chernikov-by-abelian is itself Chernikov-by-abelian [Arch. Math. 51, 193-197 (1988; Zbl 0632.20018)]. Here they show that if ${\cal X}$ is the class of groups with Chernikov layers (CL-groups) or the union of the classes of CL- groups and Chernikov-by-abelian groups then a locally graded group in which every proper subgroup is an ${\cal X}$-group is itself an ${\cal X}$-group. From this they deduce results concerning minimal non-FL- groups; that is, groups in which every proper subgroup has finite layers.
[M.J.Tomkinson]

MSC 2000:: *20F24 FC-groups and generalizations
20E15 Chains and lattices of subgroups of groups
20E07 Subgroup theorems (group theory)

Keywords: CC-group; groups with finite layers; minimal non-FC-group; groups with Chernikov layers; CL-groups; Chernikov-by-abelian groups; locally graded group; minimal non-FL-groups

Citations: Zbl 0645.20016; Zbl 0632.20018

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