On the sum of non-cyclic subgroups order in a finite group
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.).
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Cited Times [WOS]:0
|Document Type||Journal Article|
|Department||SUSTech International Center for Mathematics|
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
|First Author Affilication||SUSTech International Center for Mathematics|
|Corresponding Author Affilication||SUSTech International Center for Mathematics|
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).
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