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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Minimal relative relation modules of finite $p$-groups


Author: Mohammad Yamin
Journal: Proc. Amer. Math. Soc. 118 (1993), 1-3
MSC: Primary 20J05; Secondary 20C05
DOI: https://doi.org/10.1090/S0002-9939-1993-1086347-3
MathSciNet review: 1086347
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Abstract: Consider $1 \to S \to E \to G \to 1$, where $G$ is a finite $p$-group generated by ${g_i},\;1 \leqslant i \leqslant d$, and $E$ a free product of cyclic groups $\langle {g_i}\rangle ,1 \leqslant i \leqslant d$. If $d$ is the minimum number of generators for $G$, then we prove that the largest elementary abelian $p$-quotient $S/{S’}{S^p}$, regarded as an ${\mathbb {F}_p}G$-module via conjugation in $E$, is nonprojective and indecomposable.


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Article copyright: © Copyright 1993 American Mathematical Society