The average element order and the number of conjugacy classes of finite groups
| Autor: | Mohammad Zarrin, Evgeny Khukhro, Alexander Moretó |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
20D15
20C15 20E45 Finite group Polynomial Algebra and Number Theory Group (mathematics) 010102 general mathematics Group Theory (math.GR) 01 natural sciences Upper and lower bounds Element Order Combinatorics Conjugacy class 0103 physical sciences FOS: Mathematics Order (group theory) 010307 mathematical physics 0101 mathematics Abelian group Mathematics - Group Theory G110 Pure Mathematics Mathematics |
| DOI: | 10.48550/arxiv.2009.08226 |
| Popis: | Let o ( G ) be the average order of the elements of G, where G is a finite group. We show that there is no polynomial lower bound for o ( G ) in terms of o ( N ) , where N ⊴ G , even when G is a prime-power order group and N is abelian. This gives a negative answer to a question of A. Jaikin-Zapirain. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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