On pairs of non-abelian finite p-groups

Khamseh, Elaheh

doi:10.22061/jdma.2024.10706.1068

On pairs of non-abelian finite p-groups

Document Type : Special Issue of the IGTC 16

Author

Elaheh Khamseh

Department of Mathematics, Islamic Azad University, Shahr-e-Qods Branch, Tehran, Iran.

10.22061/jdma.2024.10706.1068

Abstract

Let (N;G) be a pair of non-abelian finite p-groups and K be a
normal subgroup of G such that G = N \times K, where K is a d-generator group
of order pm. Moreover, let |N| = p^n and {N'| = p^k. Then |M(N;G)|=
p^{1/2 (n-1)(n-2)+1+(n-1)m-s'}
, where M(N;G) is the Schur multiplier of the
pair (N;G) and s0 is a non-negative integer. In this paper, the non-abelian
pairs (N;G) for s0 = 0; 1; 2; 3 are characterized.

Keywords