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Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
Published on: February 15, 2016
Strongly Base-Two Groups
Timothy C Burness1, Robert M Guralnick2
1School of Mathematics, University of Bristol, Bristol, BS8 1UG UK.
Abstract:
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 be the number of conjugacy classes of core-free subgroups H of G with . We say that G is a strongly base-two group if , 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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