On a problem from the Kourovka Notebook

2015/08/05 by Xiaoyu Chen, Chen, Xiaoyu
Computer Science · Engineering · Mathematics · #20D10 #20D20 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1508.00957

openalex publication_date 2015/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this manuscript, a solution to Problem 18.91(b) in the Kourovka Notebook is given by proving the following theorem. Let P be a Sylow p-subgroup of a group G with |P| = pⁿ. Suppose that there is an integer k such that 1 < k < n and every subgroup of P of order p^k is S-propermutable in G, and also, in the case that p=2, k = 1 and P is non-abelian, every cyclic subgroup of P of order 4 is S-propermutable in G. Then G is p-nilpotent.

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