Notes on B -groups Full article
| Journal |
Communications in Algebra
ISSN: 0092-7872 , E-ISSN: 1532-4125 |
||||||
|---|---|---|---|---|---|---|---|
| Output data | Year: 2025, Number: 53, Pages: 4398–4402 Pages count : 6 DOI: 10.1080/00927872.2025.2484425 | ||||||
| Tags | Permutation groups, Schur rings, Cayley graphs | ||||||
| Authors |
|
||||||
| Affiliations |
|
Abstract:
Following Wielandt, a finite group G is called a B-group (Burnside group) if every primitive group containing a regular subgroup isomorphic to G is doubly transitive. Using a method of Schur rings, Wielandt proved that every abelian group of composite order which has at least one cyclic Sylow subgroup is a B group. Since then, other infinite families of B-groups were found by the same method. A simple analysis of the proofs of these results shows that in all of them a stronger statement was proved for the group G under consideration: everyprimitiveSchurringoverGistrivial.AfinitegroupGpossessingthelatter property, we call BS-group (Burnside-Schurgroup). In the present note, we give infinitely many examples of B-groups which are not BS-groups.
Cite:
Ponomarenko I.
, Ryabov G.
Notes on B -groups
Communications in Algebra. 2025. N53. P.4398–4402. DOI: 10.1080/00927872.2025.2484425 WOS Scopus OpenAlex
Notes on B -groups
Communications in Algebra. 2025. N53. P.4398–4402. DOI: 10.1080/00927872.2025.2484425 WOS Scopus OpenAlex
Dates:
| Submitted: | Oct 30, 2024 |
| Accepted: | Mar 17, 2025 |
| Published online: | Apr 21, 2025 |
Identifiers:
| Web of science: | WOS:001471238300001 |
| Scopus: | 2-s2.0-105003228188 |
| OpenAlex: | W4409625239 |