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 α ( G ) be the number of conjugacy classes of core-free subgroups H of G with b ( G , H ) ≥ 3 . We say that G is a strongly base-two group if α ( G ) ≤ 1 , which means...

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Bibliographic Details
Published in:Vietnam journal of mathematics 2023, Vol.51 (3), p.657-683
Main Authors: Burness, Timothy C., Guralnick, Robert M.
Format: Article
Language:English
Subjects:
Group theory
Mathematics
Mathematics and Statistics
Original
Original Article
Permutations
Subgroups
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Summary: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 α ( G ) be the number of conjugacy classes of core-free subgroups H of G with b ( G , H ) ≥ 3 . We say that G is a strongly base-two group if α ( G ) ≤ 1 , 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.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-023-00628-0