The multiplicator of finite nilpotent groups
- 1 August 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 3 (1) , 1-8
- https://doi.org/10.1017/s0004972700045597
Abstract
Let G be a group and M a G-module; then d(G) denotes the minimal number of generators of G and dG(M) the minimal number of generators over ZG of M. For G a finite nilpotent group let G = F/R, F free, be a presentation for G; then it is shown that d(R/[F, R]) = dG(R/[R, R]), that is d(G) + d(M(G)) = dG(R/R′), where M(G) denotes the Schur multiplicator of G.Keywords
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