Finite p-groups of nilpotency class 3 with two conjugacy class sizes

Naik, Tushar Kanta; Kitture, Rahul Dattatraya; Yadav, Manoj K.

doi:10.1007/s11856-020-1990-3

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2023

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Cited by 4 publications

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“…According to it, the group G is a semidirect product of the normal p ′ -subgroup of G and a p-subgroup P . The structure of P is generally clear (see [5,13]), it would be interesting to have an answer to the following question. It is easy to see that groups with the R(p) * * property are quite common.…”

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confidence: 99%

On $p$-index extremal groups

Vasil’ev¹,

Gorshkov²

2023

Preprint

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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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confidence: 99%