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Schur multiplicators of finite p-groups with fixed coclass

Research paper by Bettina Eick

Indexed on: 14 Aug '08Published on: 14 Aug '08Published in: Israel Journal of Mathematics



Abstract

We investigate the Schur multiplicators M(G) of p-groups G using coclass theory. For p > 2 we show that there are at most finitely many p-groups G of coclass r with |M(G)| ≤ s for every r and s. We observe that this is not true for p = 2 by constructing infinite series of 2-groups G with coclass r and |M(G)| = 1. We investigate the Schur multiplicators of the 2-groups of coclass r further.