Complexity and varieties for infinite groups. II
[For part I see the preceding review Zbl 0886.20002.] The author studies the properties of the categories \(\text{Mod}(kG)\), \(\text{mod}(kG)\), \(\text{StMod}(kG)\), \(\text{stmod}(kG)\) for an \(LH{\mathfrak F}\)-group \(G\) and varieties of such modules. As application of these results he obtains the following important result. Theorem 19.1. Let \(G\) be an \(LH{\mathfrak F}\)-group of type \(FP_\infty\). Then there are only finitely many conjugacy classes in \(G\) of finite elementary abelian subgroups. The author notes that it is possible to obtain this theorem from results of Henn (unpublished) and Kropholler and Mislin.
scientific article; zbMATH DE number 1051522
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