Strongly Base-Two Groups

Let G be a finite group, let H be a core-free subgroup and let b(G, H) denote the base size for the action of G on G/H. Let [Formula: see text] be the number of conjugacy classes of core-free subgroups H of G with [Formula: see text] . We say that G is a strongly base-two group if [Formula: see text...

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Detalles Bibliográficos
Autores principales: Burness, Timothy C., Guralnick, Robert M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Nature Singapore 2023
Materias:
Original Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10444712/
https://www.ncbi.nlm.nih.gov/pubmed/37621861
http://dx.doi.org/10.1007/s10013-023-00628-0
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author Burness, Timothy C.
Guralnick, Robert M.
author_facet Burness, Timothy C.
Guralnick, Robert M.
author_sort Burness, Timothy C.
collection PubMed
description Let G be a finite group, let H be a core-free subgroup and let b(G, H) denote the base size for the action of G on G/H. Let [Formula: see text] be the number of conjugacy classes of core-free subgroups H of G with [Formula: see text] . We say that G is a strongly base-two group if [Formula: see text] , which means that almost every faithful transitive permutation representation of G has base size 2. In this paper, we study the strongly base-two finite groups with trivial Frattini subgroup.
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spelling pubmed-104447122023-08-24 Strongly Base-Two Groups Burness, Timothy C. Guralnick, Robert M. Vietnam J Math Original Article Let G be a finite group, let H be a core-free subgroup and let b(G, H) denote the base size for the action of G on G/H. Let [Formula: see text] be the number of conjugacy classes of core-free subgroups H of G with [Formula: see text] . We say that G is a strongly base-two group if [Formula: see text] , which means that almost every faithful transitive permutation representation of G has base size 2. In this paper, we study the strongly base-two finite groups with trivial Frattini subgroup. Springer Nature Singapore 2023-05-10 2023 /pmc/articles/PMC10444712/ /pubmed/37621861 http://dx.doi.org/10.1007/s10013-023-00628-0 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Article
Burness, Timothy C.
Guralnick, Robert M.
Strongly Base-Two Groups
title Strongly Base-Two Groups
title_full Strongly Base-Two Groups
title_fullStr Strongly Base-Two Groups
title_full_unstemmed Strongly Base-Two Groups
title_short Strongly Base-Two Groups
title_sort strongly base-two groups
topic Original Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10444712/
https://www.ncbi.nlm.nih.gov/pubmed/37621861
http://dx.doi.org/10.1007/s10013-023-00628-0
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