6533b870fe1ef96bd12d071d
RESEARCH PRODUCT
Near abelian profinite groups
Francesco G. RussoKarl H. Hofmannsubject
Pure mathematicsProfinite groupApplied MathematicsGeneral Mathematicstopologically quasihamiltonian groupProjective covermodular groupcompact groupsSettore MAT/03 - GeometriaAbelian groupMathematicspro-$p$-groupdescription
Abstract A compact p-group G (p prime) is called near abelian if it contains an abelian normal subgroup A such that G/A has a dense cyclic subgroup and that every closed subgroup of A is normal in G. We relate near abelian groups to a class of compact groups, which are rich in permuting subgroups. A compact group is called quasihamiltonian (or modular) if every pair of compact subgroups commutes setwise. We show that for p ≠ 2 a compact p-group G is near abelian if and only if it is quasihamiltonian. The case p = 2 is discussed separately.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-12-15 |