A note on groups with finite conjugacy classes of subnormal subgroups
-
Francesco de Giovanni
and
Federica Saccomanno
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.
This work was partially supported by MIUR-PRIN 2009 (Teoria dei Gruppi e Applicazioni). The first author is a member of GNSAGA (INdAM).
References
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© 2017 Mathematical Institute Slovak Academy of Sciences
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- Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
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