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- Title
A NOTE ON GROUPS WITH FINITE CONJUGACY CLASSES OF SUBNORMAL SUBGROUPS.
- Authors
DE GIOVANNI, FRANCESCO; SACCOMANNO, FEDERICA
- Abstract
A group G is said to be a V -group if every subnormal subgroup of G has only finitely many conjugates. It is proved here that if G is a group admitting an ascending normal series whose factors have finite rank, and all proper subgroups of G have the V -property, then G itself is a V -group, provided that G belongs to a suitable class of generalized soluble groups, containing in particular all locally (soluble-by-finite) groups. On the other hand, an example shows that there exist periodic metabelian minimal non-V groups.
- Subjects
FINITE groups; CONJUGACY classes; SUBNORMAL operators; FREE metabelian groups; SOLVABLE groups
- Publication
Mathematica Slovaca, 2017, Vol 67, Issue 2, p387
- ISSN
0139-9918
- Publication type
Article
- DOI
10.1515/ms-2016-0274