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- Title
On the average codegree of a finite group.
- Authors
Wang, Zhongbi; Qian, Guohua; Lv, Heng; Chen, Guiyun
- Abstract
Let G be a finite group, we define the average codegree of the irreducible characters of G as acod (G) = 1 | Irr (G) | ∑ χ ∈ Irr (G) cod (χ) , where cod (χ) = | G : ker χ | χ (1) . We prove that if G is non-solvable, then acod (G) ≥ 6 8 / 5 , and the equality holds if and only if G ≅ A 5 . Also, we show that if G is non-supersolvable, then acod (G) ≥ 1 1 / 4 , and the equality holds if and only if G ≅ A 4 . In addition, we obtain that if p is the smallest prime divisor of | G | , then acod (G) < p if and only if G is an elementary abelian p -group.
- Subjects
FINITE groups; SMALL divisors; ABELIAN groups
- Publication
Journal of Algebra & Its Applications, 2024, Vol 23, Issue 5, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498824501020