Classification of EPPO-groups with seven non-central conjugacy classes

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Foruzanfar Zeinab; REZAEI MEHDI

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Journal Paper

Paper Information

Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2022 | Volume:8 | Issue:36 Page(s): 115-128

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Information Journal Paper

Title

Classification of EPPO-groups with seven non-central conjugacy classes

Author(s)

Foruzanfar Zeinab | REZAEI MEHDI | Issue Writer Certificate

Keywords

Conjugacy class

Sylow p-subgroup

Frobenius group

Order

Abstract

Let G be a finite group and Z(G) be a subgroup of it. Suppose that for the finite group G, Pi_e(G) denotes the set of Orders of elements of G. Then G is an EPPO-group if the Orders of its elements are non-negative powers of primes. Also, for a subset A of G, let r_G(A) be the number of Conjugacy classes of G that intersect A non-trivially. The purpose of this paper is to classify all finite EPPO-groups with the property r_G(G-Z(G))=7. We first verify the case where Z(G)=1. Then we verify the case where G/Z(G) is abelian. After that, we consider the case where G/Z(G) is non-abelian. We verify this case in three subcases where G/Z(G) is a p-group, a Frobenius group or a 2-Frobenius group. In fact, we show that the only groups which satisfy the intended property are the groups that are attained in the case Z(G)=1 and all of these groups are Frobenius groups.

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APA: Copy

Foruzanfar, Zeinab, & REZAEI, MEHDI. (2022). Classification of EPPO-groups with seven non-central conjugacy classes. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 8(36 ), 115-128. SID. https://sid.ir/paper/1064706/en

Vancouver: Copy

Foruzanfar Zeinab, REZAEI MEHDI. Classification of EPPO-groups with seven non-central conjugacy classes. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2022;8(36 ):115-128. Available from: https://sid.ir/paper/1064706/en

IEEE: Copy

Zeinab Foruzanfar, and MEHDI REZAEI, “Classification of EPPO-groups with seven non-central conjugacy classes,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 8, no. 36 , pp. 115–128, 2022, [Online]. Available: https://sid.ir/paper/1064706/en

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