Pavel Shumyatsky, Pavel Zalesskii, Theo Zapata
Published 2018-07-06Version 1
The article deals with profinite groups in which the centralizers are abelian (CA-groups), that is, with profinite commutativity-transitive groups. It is shown that such groups are virtually pronilpotent. More precisely, let G be a profinite CA-group. It is shown that G has a normal open subgroup N which is either abelian or pro-p. Further, a rather detailed information about the finite quotient G/N is obtained.
Norm rigidity for arithmetic and profinite groups
Centralizers of Subsystems of Fusion Systems
On solubility of groups with finitely many centralizers
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