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- W2575209966 abstract "In [1, 8.80], we asked whether it is true that, if G is a locally finite group with a Chernikov maximal subgroup, then G is locally soluble. In this paper we prove a stronger result, and in fact give an essentially complete description of all locally finite groups with such a maximal subgroup. Of course, if G is a Chernikov group itself, then the maximal subgroups of G, if any, will be Chernikov. Other examples are the groups constructed by Charin [2, 1.H.3]. The simplest version is obtained as follows. Let p and q be primes, and let K be the algebraic closure of the field lFp with p elements. Let Q be the multipficative group consisting of all qth roots of 1 in K (n = 1,2,...), and let V be the subfield IFp[Q] generated by Q. Then Q acts faithfully and irreducibly on V (considered as an additive group). The semidirect product G = VQ has V as its unique minimal normal subgroup and Q as a Chernikov maximal subgroup. Similar examples can be obtained if Q is replaced by certain other Chernikov groups, and these two types of examples essentially exhaust all the possibilities." @default.
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- W2575209966 date "1998-01-01" @default.
- W2575209966 modified "2023-09-27" @default.
- W2575209966 title "ON LOCALLY FINITE GROUPS WITH" @default.
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