An affirmative answer to the Jainkin-Zapirain's question
Group Theory
2019-11-19 v1
Abstract
If X is a non-empty subset of a finite group G, we denote by o(x) the order of x in G. Then we put The number o(X) is called the average order of X. Zapirain in 2011 , posed the following question: Let G be a finite (p-) group and N a normal (abelian) subgroup of G. Is it true that o(G) ? Here, we will improve his question and confirm it.
Cite
@article{arxiv.1911.07641,
title = {An affirmative answer to the Jainkin-Zapirain's question},
author = {M. Zarrin},
journal= {arXiv preprint arXiv:1911.07641},
year = {2019}
}
Comments
3 pages