On the sum of non-cyclic subgroups order in a finite group

Meng，Wei1,2; Lu，Jiakuan3

2023

10.1080/00927872.2023.2255673

Communications in Algebra   Impact Factor & Quartile

0092-7872

1532-4125

Let G be a finite group and (Formula presented.) is non-cyclic}. In this paper, we show that some arithmetical conditions of (Formula presented.) influence the structure of G. Firstly, we prove that if (Formula presented.), then G is solvable. Secondly, we determine the structure of finite groups with (Formula presented.). Moreover, we prove that if (Formula presented.), then G is supersolvable, and we also determine the structure of finite groups G with (Formula presented.). Finally, we show that (Formula presented.) does not imply the supersolvability of G for any constant (Formula presented.).

Non-cyclic subgroups subgroup orders supersolvable groups

SCI

English

Corresponding

Mathematics

Mathematics

WOS:001066144700001

TAYLOR & FRANCIS INC

MATHEMATICS

2-s2.0-85170669028

Scopus

1.School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin,China
2.SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,China
3.School of Mathematics and Statistics,Guangxi Normal University,Guilin,Guangxi,China

Meng，Wei,Lu，Jiakuan. On the sum of non-cyclic subgroups order in a finite group[J]. Communications in Algebra,2023.

Meng，Wei,&Lu，Jiakuan.(2023).On the sum of non-cyclic subgroups order in a finite group.Communications in Algebra.

Meng，Wei,et al."On the sum of non-cyclic subgroups order in a finite group".Communications in Algebra (2023).