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Results tagged with finite-groups
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user 38708
Questions on group theory which concern finite groups.
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votes
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answer
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Index of $Z(G)$ in the centralizer of an element of a finite 2-group
Let $G$ be a finite 2-group. Let $x$ be a non-central element of $G$ such that $C_G(x)\leq cl(x)\cup Z(G)$ where $cl(x)$ denotes the conjugacy class of $x$ in $G$.
Is it true that $|C_G(x):Z(G)|=2$?
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