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- Title
On embedding theorems for X-subgroups.
- Authors
Guo, Wenbin; Revin, Danila O.; Vasil'ev, Andrey V.
- Abstract
Let X be a class of finite groups closed under subgroups, homomorphic images, and extensions. We study the question which goes back to the lectures of H. Wielandt in 1963–1964: Given an X -subgroup K and a maximal X -subgroup H, is it possible to detect embeddability of K in H (up to conjugacy) by their projections into the factors of a fixed subnormal series? On the one hand, we construct examples where K has the same projections as some subgroup of H but is not conjugate to any subgroup of H. On the other hand, we prove that if K normalizes the projections of a subgroup H, then K is conjugate to a subgroup of H even in the more general case when H is a submaximal X -subgroup.
- Publication
Archiv der Mathematik, 2023, Vol 121, Issue 1, p11
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-023-01865-y