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Proceedings of the American Mathematical Society

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

 

 

Groups of finite weight


Author: A. H. Rhemtulla
Journal: Proc. Amer. Math. Soc. 81 (1981), 191-192
MSC: Primary 20F05
DOI: https://doi.org/10.1090/S0002-9939-1981-0593454-X
MathSciNet review: 593454
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Abstract: If $ N$ is a group and $ E$ is a group of operators on $ N$ then write $ {d_E}(N)$ for the minimum number of elements needed to generate $ N$ as an $ E$-group. It is shown that if $ N$ is a normal subgroup of $ E$ and $ E$ acts on $ N$ by conjugation, then $ {d_E}(N) = {d_E}(N/N')$ if $ {d_E}(N)$ is finite and there does not exist an infinite descending series of $ E$-normal subgroups $ N' = {C_0} > {C_1} > \cdots $ with each $ {C_i}/{C_{i + 1}}$ perfect. Both these conditions are, in general, necessary.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0593454-X
Article copyright: © Copyright 1981 American Mathematical Society