×

Generating numbers for wreath products. (English) Zbl 0827.20040

For any group \(G\), \(d(G)\) denotes the minimal number of generators. For groups \(A\), \(B\), \(A\wr B\) denotes the wreath product of \(A\) by \(B\). The author proves the following Theorem: For every positive integer \(m\) there exists a group \(A\) with \(d(A)=m\) and a cyclic group \(B\) such that \(d(A\wr B)=2\).

MSC:

20E22 Extensions, wreath products, and other compositions of groups
20F05 Generators, relations, and presentations of groups
PDFBibTeX XMLCite
Full Text: Numdam EuDML

References:

[1] P. Hall , The Eulerian functions of a group , Quart. J. Math. ( Oxford ), 7 ( 1936 ), pp. 134 - 151 . JFM 62.0082.02 · JFM 62.0082.02
[2] J. Wiegold , Growth sequences of finite groups , J. Austral. Math. Soc. , 17 , pp. 133 - 141 . MR 349841 | Zbl 0286.20025 · Zbl 0286.20025 · doi:10.1017/S1446788700016712
[3] H. Wielandt , Finite Permutation Groups, Lectures , University of Tübingen ( 1954 / 55 ); English trans., Academic Press , New York ( 1964 ). MR 183775 | Zbl 0138.02501 · Zbl 0138.02501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.