Structure of Relative Relation Modules of Finite Groups

Mohammad Yamin () and P. K. Sharma ()
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Mohammad Yamin: King Abdulaziz University
P. K. Sharma: D.A.V. College

A chapter in International Conference on Mathematical Sciences and Statistics 2013, 2014, pp 265-274 from Springer

Abstract: Abstract Decomposability properties of modules of finite groups are known to be useful in describing the structure of certain groups. 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 $F_{p}G$ -module. Whenever E is a free group, $\hat{S}$ is called relation module (modulo p) of G; in general $\hat{S}$ is called relative relation module (modulo p). Many researchers have studied relation and relative relation modules. In this paper, we describe the structure of relative relation modules of finite groups, and in particular, those of abelian p-groups. We also describe the decomposition of relative relation modules of SL(2,p) and PSL(2,p). Decomposition of $\hat{S}$ described in this paper may be useful in studying factor group of PSL(2, Z), which is an interesting problem in its own right.

Keywords: Factors Study Group; Free Product; Decomposability Property; Krull-Schmidt Theorem; Principal Indecomposable Modules (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-4585-33-0_27

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DOI: 10.1007/978-981-4585-33-0_27

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