Profinite groups with restricted centralizers of commutators
2019 ◽
Vol 150
(5)
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pp. 2301-2321
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AbstractA group G has restricted centralizers if for each g in G the centralizer $C_G(g)$ either is finite or has finite index in G. A theorem of Shalev states that a profinite group with restricted centralizers is abelian-by-finite. In the present paper we handle profinite groups with restricted centralizers of word-values. We show that if w is a multilinear commutator word and G a profinite group with restricted centralizers of w-values, then the verbal subgroup w(G) is abelian-by-finite.
2014 ◽
Vol 97
(3)
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pp. 343-364
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2013 ◽
Vol 23
(01)
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pp. 81-89
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2012 ◽
Vol 93
(3)
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pp. 325-332
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2015 ◽
Vol 59
(2)
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pp. 533-539
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2016 ◽
Vol 26
(05)
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pp. 973-983
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