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arXiv · 2305.06184

Groups with anticentral elements

Frieder Ladisch
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Abstract

We study finite groups $G$ with elements $g$ such that $\lvert \mathbf{C}_G(g)\rvert = \lvert G:G' \rvert$. (Such elements generalize fixed-point-free automorphisms of finite groups.) We show that these groups have a unique conjugacy class of nilpotent supplements for the commutator subgroup and, using the classification of finite simple groups, that these groups are solvable.

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Frieder Ladisch. 2023-05-10. Groups with anticentral elements. https://doi.org/10.1080/00927870802108106

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