Article ID Journal Published Year Pages File Type
8895801 Journal of Algebra 2018 8 Pages PDF
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.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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