Conjugacy classes and finite $p$-groups

Details Conjugacy classes and finite $p$-groups Conjugacy classes and finite $p$-groups

2005-04-07

arxiv.org/abs/math/0504156v1

Mathematics

Group Theory

Scientific paper

Let $G$ be a finite $p$-group, where $p$ is a prime number, and $a\in G$.
Denote by $\Cl(a)=\{gag^{-1}\mid g\in G\}$ the conjugacy class of $a$ in $G$.
Assume that $|\Cl(a)|=p^n$. Then $\Cl(a)\Cl(a^{-1})=\{xy\mid x\in \Cl(a), y\in
\Cl(a^{-1})\}$ is the union of at least $n(p-1)+1$ distinct conjugacy classes
of $G$.

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