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arXiv · 2301.09265

On $p$-index extremal groups

Andrey V. Vasil'ev·Ilya B. Gorshkov
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Abstract

The question on connection between the structure of a finite group $G$ and the properties of the indices of elements of $G$ has been a popular research topic for many years. The $p$-index $|x^G|_p$ of an element $x$ of a group $G$ is the $p$-part of its index $|x^G|=|G:C_G(x)|$. The presented short note describes some new results and open problems in this direction, united by the concept of the $p$-index of a group element.

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Andrey V. Vasil'ev, Ilya B. Gorshkov. 2023-01-23. On $p$-index extremal groups. https://doi.org/10.1007/s10469-023-09728-9

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