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math.GR2026

Sectionally indecomposable groups

Andrea Lucchini, Nowras Otmen

We introduce the notion of sectional indecomposability and study it for finite groups: a group $H$ is sectionally indecomposable if, whenever $H$ is a section of a direct product $…

math.GR2026

On probabilistic identities and coset identities in pro- $p$ groups

Steffen Kionke, Nowras Otmen, Tommaso Toti +2

It is shown that a probabilistic identity on a $I ¨ $ -compact $K$ -analytic group $G$ , $K$ a non-archimedean local field, is a coset identity. As an application, one concludes that co…

math.GR2025

Profinite groups with many elements with large nilpotentizer and generalizations

Martino Garonzi, Andrea Lucchini, Nowras Otmen

Given a profinite group $G$ and a family $F$ of finite groups closed under taking subgroups, direct products and quotients, denote by $F (G)$ the set of elements…

math.GR2024

$p$ -elements in profinite groups

Andrea Lucchini, Nowras Otmen

We investigate some properties of the $p$ -elements of a profinite group $G$ . We prove that if $p$ is odd and the probability that a randomly chosen element of $G$ is a $p$ -element…

Sectionally indecomposable groups

On probabilistic identities and coset identities in pro-p groups

Profinite groups with many elements with large nilpotentizer and generalizations

p-elements in profinite groups

On probabilistic identities and coset identities in pro- $p$ groups

$p$ -elements in profinite groups