On a Finite Group with Restriction on Set of Conjugacy Classes Size

Autor: I. B. Gorshkov
Rok vydání: 2019
Předmět:
Zdroj: Bulletin of the Malaysian Mathematical Sciences Society. 43:2995-3005
ISSN: 2180-4206
0126-6705
DOI: 10.1007/s40840-019-00843-4
Popis: The greatest power of a prime p dividing the natural number n will be denoted by $$n_p$$. For a set of primes $$\pi $$ and a natural number n we will denote $$n_{\pi }=\prod _{p\in \pi }n_p$$. Let G be a finite group with trivial center, and $$p,q>5$$ be distinct prime divisors of |G|. We prove that if for every nonunity conjugacy classes size $$\alpha $$, it is true that $$\alpha _{\{p,q\}}\in \{p^n,q^m,p^nq^m\}$$, where n and m depend only on p and q, then $$|G|_{\{p,q\}}=p^nq^m$$, and $$C_G(g)\cap C_G(h)=1$$ for every p-element g and every q-element h.
Databáze: OpenAIRE
Externí odkaz: