Relative relation modules of finite elementary abelian $p$-groups
Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 1205-1210
https://doi.org/10.4134/BKMS.2014.51.4.1205
Published online July 31, 2014
Mohammad Yamin and Poonam Kumar Sharma
King Abdulaziz University, D.A.V. College
Abstract : Let $E$ be a free product of a finite number of cyclic groups, and $S$ a normal subgroup of E such that $E/S \cong G$ is finite. For a prime $p$, $\hat{S} = S/S^{'}S^{p}$ may be regarded as an $F_{p}G$-module via conjugation in $E$. The aim of this article is to prove that $\hat{S}$ is decomposable into two indecomposable modules for finite elementary abelian $p$-groups $G$.
Keywords : free groups, free products, $p$-groups, modules, relation modules
MSC numbers : 20C05, 16D10, 16D70
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