Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895801 | Journal of Algebra | 2018 | 8 Pages |
Abstract
Bouc proposed the following conjecture: a finite group G is nilpotent if and only if its largest quotient B-group β(G) is nilpotent. And Thévenaz proposed another conjecture: a finite group G is solvable if and only if its largest quotient B-group β(G) is solvable. Bouc has proven that his conjecture holds when G is solvable. In this paper, we consider some cases when G is not solvable. Let S be a nonabelian simple group except the Chevalley groups An(q), Dn(q), E6(q), and An2(q), if the group G has exactly one composition factor isomorphic to S, then β(G) is not solvable, of course, is not nilpotent. That means we prove the conjectures in these cases.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xingzhong Xu, Jiping Zhang,