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arXiv · 1801.05975

Groups whose elements are not conjugate to their powers

Andreas Bächle·Benjamin Sambale
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Abstract

We call a finite group irrational if none of its elements is conjugate to a distinct power of itself. We prove that those groups are solvable and describe certain classes of these groups, where the above property is only required for $p$-elements, for $p$ from a prescribed set of primes.

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Andreas Bächle, Benjamin Sambale. 2018-01-18. Groups whose elements are not conjugate to their powers. https://doi.org/10.1007/s00013-018-1155-3

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