6533b82ffe1ef96bd129510a
RESEARCH PRODUCT
The average element order and the number of conjugacy classes of finite groups
Mohammad ZarrinEvgeny KhukhroAlexander Moretósubject
20D15 20C15 20E45Finite groupPolynomialAlgebra and Number TheoryGroup (mathematics)010102 general mathematicsGroup Theory (math.GR)01 natural sciencesUpper and lower boundsElement OrderCombinatoricsConjugacy class0103 physical sciencesFOS: MathematicsOrder (group theory)010307 mathematical physics0101 mathematicsAbelian groupMathematics - Group TheoryG110 Pure MathematicsMathematicsdescription
Abstract 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-03-01 |