Some results of $\alpha$-coset groups

Document Type : Research Paper

Authors

1 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

2 Department of Mathematics, Khayyam University, Mashhad, Iran\ Department of Pure Mathematics, Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O.Box 1159, Mashhad, 91775, Iran.

3 Department of Mathematics, Khayyam University, Mashhad, Iran.

Abstract

We call $G$ to be an $\alpha$-coset group, if it contains a proper $\alpha$-invariant normal subgroup $N$ such that $Nx^\alpha =\{x^g~|~ g\in G\}$, for some automorphism $\alpha$ of $G$ and any $x \in G\setminus N$. Clearly, if $\alpha$ is identity automorphism of $G$, one obtains the notion of con-cos groups, which was first introduced by Muktibodh in 2006.
In the present article, we discuss some properties of the new notion. Also, we introduce the concept of $\alpha$-Camina groups and give its connection with the groups of property $\mathcal P$, where $\mathcal P$ is the class of all finite groups such that their $\alpha$-centres are the same as $\alpha$-commutator subgroups of order $p$.

Keywords

References

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Algebraic Structures and Their Applications
Volume 10, Issue 1
February 2023
Pages 87-93

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