It is shown that a finite group G has four relative commutativity degrees if and only if G/Z（G） is a p-group of order p3 and G has no abelian maximal subgroups, or G/Z（G） is a Frobenius group with Frobenius kernel...It is shown that a finite group G has four relative commutativity degrees if and only if G/Z（G） is a p-group of order p3 and G has no abelian maximal subgroups, or G/Z（G） is a Frobenius group with Frobenius kernel and complement isomorphic to Zp × Zp and Zq, respectively, and the Sylow p-subgroup of G is abelian, where p and q are distinct primes.展开更多
Let p be a prime number and f_2(G) be the number of factorizations G = AB of the group G, where A, B are subgroups of G. Let G be a class of finite p-groups as follows,G = a, b | a^(p^n)= b^(p^m)= 1, a^b= a^(p^(n-1)+1...Let p be a prime number and f_2(G) be the number of factorizations G = AB of the group G, where A, B are subgroups of G. Let G be a class of finite p-groups as follows,G = a, b | a^(p^n)= b^(p^m)= 1, a^b= a^(p^(n-1)+1), where n > m ≥ 1. In this article, the factorization number f_2(G) of G is computed, improving the results of Saeedi and Farrokhi in [5].展开更多
文摘It is shown that a finite group G has four relative commutativity degrees if and only if G/Z（G） is a p-group of order p3 and G has no abelian maximal subgroups, or G/Z（G） is a Frobenius group with Frobenius kernel and complement isomorphic to Zp × Zp and Zq, respectively, and the Sylow p-subgroup of G is abelian, where p and q are distinct primes.
基金Supported by National Natural Science Foundation of China(11601121)Henan Provincial Natural Science Foundation of China(162300410066)
文摘Let p be a prime number and f_2(G) be the number of factorizations G = AB of the group G, where A, B are subgroups of G. Let G be a class of finite p-groups as follows,G = a, b | a^(p^n)= b^(p^m)= 1, a^b= a^(p^(n-1)+1), where n > m ≥ 1. In this article, the factorization number f_2(G) of G is computed, improving the results of Saeedi and Farrokhi in [5].
