On groups of finite Prüfer rank II
Copyright policy )On groups of finite Prüfer rank II
Let G be a group of finite (Prüfer) rank and \pi any finite set of primes. We prove, in particular, that G contains a characteristic subgroup H of finite index such that for every normal subgroup Y of H of finite index the maximal normal \pi -subgroup of H/Y lies in the hypercentre of H/Y , so in particular all finite \pi -images of H are nilpotent.
- Queen Mary University of London United Kingdom
nilpotent group, General structure theorems for groups, Generalizations of solvable and nilpotent groups, groups of finite Prüfer rank, Periodic groups; locally finite groups, Subgroup theorems; subgroup growth, finite residual rank, Other classes of groups defined by subgroup chains, Residual properties and generalizations; residually finite groups
nilpotent group, General structure theorems for groups, Generalizations of solvable and nilpotent groups, groups of finite Prüfer rank, Periodic groups; locally finite groups, Subgroup theorems; subgroup growth, finite residual rank, Other classes of groups defined by subgroup chains, Residual properties and generalizations; residually finite groups
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