A $p$-nilpotency criterion for finite groups

TL;DR

This paper establishes a new criterion for determining p-nilpotency in finite groups based on element orders in specific sections, extending previous nilpotency criteria by Te2rne2uceanu.

Contribution

It introduces a novel p-nilpotency criterion for finite groups using element orders of p'-reduced sections, generalizing earlier results.

Findings

Provides a new p-nilpotency criterion based on element orders.

Extends Te2rne2uceanu's nilpotency criterion.

Offers a broader framework for analyzing finite group structure.

Abstract

We prove a $p$-nilpotency criterion for finite groups in terms of the element orders of its $p'$-reduced sections that extends a nilpotency criterion by T{\u{a}}rn{\u{a}}uceanu.