Zeta functions and counting finite -groups.
du Sautoy, Marcus (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Displaying similar documents to “Counting -groups and nilpotent groups”
Zeta functions and counting finite -groups.
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In this note we determine explicit formulas for the relative commutator of groups with respect to the subvarieties of -nilpotent groups and of -solvable groups. In particular these formulas give a characterization of the extensions of groups that are central relatively to these subvarieties.
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Let F C 0 be the class of all finite groups, and for each nonnegative integer n define by induction the group class FC^(n+1) consisting of all groups G such that for every element x the factor group G/CG ( <x>^G ) has the property FC^n . Thus FC^1 -groups are precisely groups with finite conjugacy classes, and the class FC^n obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of FC-groups is taken as a model, and it...