Keywords:-

Keywords: Finite Groups, Strongly Base-Two Groups, Trivial Frattini Subgroup, Core-Free Subgroups, Conjugacy Classes, Base Size, Transitive Permutation Representations.

Article Content:-

Abstract

This paper explores finite groups G with a focus on those that are strongly base-two and possess a trivial Frattini subgroup. The concept of base size, denoted by b(G, H), for the action of G on core-free subgroups H, plays a crucial role. The paper investigates the number of conjugacy classes of core-free subgroups with base size exceeding 3, denoted by α(G). A group is considered strongly base-two if α(G) ≤ 1, indicating that nearly all faithful transitive permutation representations of G exhibit a base size of 2. The study delves into the characterization of such groups, shedding light on their properties and structures.

References:-

References

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John, M. N., & U., U. I. (2023). On Strongly Base-Two Finite Groups with Trivial Frattini Subgroup: Conjugacy Classes and Core-Free Subgroup. International Journal Of Mathematics And Computer Research, 11(12), 3926-3932. https://doi.org/10.47191/ijmcr/v11i12.08