On embedding theorems for X-subgroups Full article
| Journal |
Archiv der Mathematik
ISSN: 0003-889X , E-ISSN: 1420-8938 |
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| Output data | Year: 2023, Volume: 121, Number: 1, Pages: 11–21 Pages count : 11 DOI: 10.1007/s00013-023-01865-y | ||||
| Tags | Finite group, Complete class, Maximal X-subgroup, Submaximal X-subgroup, Embedding theorems | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
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.
Cite:
Guo W.
, Revin D.O.
, Vasil’ev A.V.
On embedding theorems for X-subgroups
Archiv der Mathematik. 2023. V.121. N1. P.11–21. DOI: 10.1007/s00013-023-01865-y WOS Scopus РИНЦ OpenAlex
On embedding theorems for X-subgroups
Archiv der Mathematik. 2023. V.121. N1. P.11–21. DOI: 10.1007/s00013-023-01865-y WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 23, 2022 |
| Accepted: | May 3, 2023 |
| Published print: | Jun 13, 2023 |
| Published online: | Jun 13, 2023 |
Identifiers:
| Web of science: | WOS:001016778700002 |
| Scopus: | 2-s2.0-85163122726 |
| Elibrary: | 61989273 |
| OpenAlex: | W4380488056 |