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Proceedings of the American Mathematical Society

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



The Schur multiplicator of metacyclic groups

Author: F. Rudolf Beyl
Journal: Proc. Amer. Math. Soc. 40 (1973), 413-418
MSC: Primary 20D10
Addendum: Proc. Amer. Math. Soc. 43 (1974), 251-252.
MathSciNet review: 0325759
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Abstract: The Schur multiplicator $ {H_2}G$ of a (finite) metacyclic group $ G$ is computed with the help of the Lyndon spectral sequence. The order of $ {H_2}G$ is a useful invariant of $ G$. A metacyclic group with vanishing Schur multiplicator can be presented with two generators and two relators. A simple description of the totality of these groups is given and all such $ p$-groups are classified.

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Keywords: Metacyclic group, Schur multiplicator, Schur group, deficiency, Lyndon spectral sequence
Article copyright: © Copyright 1973 American Mathematical Society