Pavel Shumyatsky
Published 2020-04-13Version 1
For a positive integer r we prove that if G is a profinite group in which the centralizer of every nontrivial element has rank at most r, then G is either a pro-p group or a group of finite rank. Further, if G is not virtually a pro-p group, then G is virtually of rank at most r+1.
Profinite groups in which centralizers are virtually procyclic
Profinite groups with a cyclotomic $p$-orientation
Commutators and pronilpotent subgroups in profinite groups
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