International Journal of Nonlinear Analysis and Applications

On the capability, non-abelian tensor square and non-commuting graph of prime power groups

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Education, Seiyun University (SU), Yemen

2 Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran

Abstract

In this paper, we give necessary and sufficient conditions under which finite non-abelian metacyclic $p$-group ($p$ an odd prime) $G$ is capable. We also, determine the non-abelian tensor square $ G\otimes G$ for the groups of order $p^{\alpha+\beta}$ for some $\alpha, \beta\in \mathbb{N}$. Finally, we obtain some conditions on the parameters of two prime power groups $G_p$ and $G_q$ in which the groups have isomorphic non-commuting graphs.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 14 June 2025
  • Receive Date: 02 February 2023
  • Revise Date: 04 June 2024
  • Accept Date: 24 June 2024