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- Title
On the Virtual Potency of Automorphism Groups and Split Extensions.
- Authors
Azarov, D. N.
- Abstract
We obtain some sufficient conditions for potency and virtual potency for automorphism groups and the split extensions of some groups. In particular, considering a finitely generated group residually -finite for every prime , we prove that each split extension of by a torsion-free potent group is a potent group, and if the abelianization rank of is at most 2 then the automorphism group of is virtually potent. As a corollary, we derive the necessary and sufficient conditions of virtual potency for certain generalized free products and HNN-extensions.
- Subjects
AUTOMORPHISM groups; GROUP extensions (Mathematics); FINITE groups; AUTOMORPHISMS; FREE groups; MORPHISMS (Mathematics)
- Publication
Siberian Mathematical Journal, 2023, Vol 64, Issue 6, p1265
- ISSN
0037-4466
- Publication type
Article
- DOI
10.1134/S0037446623060010