Profinite groups in which centralizers are abelian

Pavel Shumyatsky; Pavel Zalesskii; Theo Zapata

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arXiv · 1807.02429

Profinite groups in which centralizers are abelian

Pavel Shumyatsky·Pavel Zalesskii·Theo Zapata

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Abstract

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.

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BibTeX RIS

Pavel Shumyatsky, Pavel Zalesskii, Theo Zapata. 2018-07-06. Profinite groups in which centralizers are abelian. https://arxiv.org/abs/1807.02429

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