A note on the conjugacy classes of non-cyclic subgroups

作者：Meng, Wei^*; Yao, Hailou; Ma, Li

来源：Communications in Algebra, 2018, 46(3): 1252-1258.

DOI：10.1080/00927872.2017.1344685

• Conjugacy class
• cyclic subgroups
• maximal groups

Let G be a finite group and delta(G) denote the number of conjugacy classes of all non-cyclic subgroups of G. The symbol pi(G) denotes the set of the prime divisors of vertical bar G vertical bar. In [7], Meng and Li showed the inequality delta(G) >= 2(vertical bar pi(G)vertical bar-2 ), where G is non-cyclic solvable group. In this paper, we describe the finite groups G such that delta(G) = 2 vertical bar pi(G)vertical bar-2. Another aim of this paper would show delta(G) >= M(G) + 2 for unsolvable groups G and the equality holds double left right arrow G congruent to A(5) or SL(2, 5), where M(G) denotes the number of conjugacy classes of all maximal subgroups of G.

• 出版日期2018
• 单位曲靖师范学院; 北京工业大学