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A class of modules over a locally finite group I

Published online by Cambridge University Press:  09 April 2009

B. Hartley
B. Hartley
Affiliation:
Mathematics InstituteUniversity of WarwickCoventryEngland.
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Let G be a locally finite group, let k be a field of characteristic p ≧ 0, and let V be a (right) kG-module, not necessarily of finite dimension over k. We say that V is an Mc-modle over kG if, for each p′-subgroup H of G, the set of centrarlizers in V of subgroups of H satisfies the minimal condition under the relation of setheoretic inclusion. Here, p′ denotes the set of all peimes different from p, and in particular 0' denotes the set of all primes. It is straightforward to verify that V is an Mc-module over kG if and only if each p′-subgroup H of G contains a finite subgroup F such that CV(F) = CV(H).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 4 , December 1973 , pp. 431 - 442
Copyright
Copyright © Australian Mathematical Society 1973

References

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