Generalized Covering Groups and Direct Limits

Behrooz Mashayekhy; Hanieh Mirebrahimi

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arXiv · 1103.5149

Generalized Covering Groups and Direct Limits

Behrooz Mashayekhy·Hanieh Mirebrahimi

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Abstract

M. R. R. Moghaddam (Monatsh. Math. 90 (1980) 37-43.) showed that the Baer invariant commutes with the direct limit of a directed system of groups. In this paper, using the generalization of Schur's formula for the structure of a $\mathcal{V}$-covering group for a Schur-Baer variety $\mathcal{V}$, we show that the structure of a $\mathcal{V}$-covering group commutes with the direct limit of a directed system, in some senses. It has a useful application in order to extend some known structures of $\mathcal{V}$-covering groups for several famous products of finitely many to an arbitrary family of groups.

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Behrooz Mashayekhy, Hanieh Mirebrahimi. 2011-03-26. Generalized Covering Groups and Direct Limits. https://arxiv.org/abs/1103.5149

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