Derived length and products of conjugacy classes
Copyright policy )Derived length and products of conjugacy classes
Let $G$ be a supersolvable group and $A$ be a conjugacy class of $G$. Observe that for some integer $��(AA^{-1})>0$, $AA^{-1}=\{a b^{-1}\mid a,b\in A\}$ is the union of $��(AA^{-1})$ distinct conjugacy classes of $G$. Set ${\bf C}_G(A)=\{g\in G\mid a^g=a\text{for all} a\in A\}$. Then the derived length of $G/{\bf C}_G(A)$ is less or equal than $2��(A A^{-1})-1$.
- University of Southern Mississippi United States
Ordinary representations and characters, 20d15, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Group Theory (math.GR), 510, finite supersolvable groups, irreducible complex characters, Physical Sciences and Mathematics, FOS: Mathematics, products of characters, derived lengths, Mathematics - Group Theory, Mathematics, Arithmetic and combinatorial problems involving abstract finite groups, Conjugacy classes for groups, products of conjugacy classes
Ordinary representations and characters, 20d15, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Group Theory (math.GR), 510, finite supersolvable groups, irreducible complex characters, Physical Sciences and Mathematics, FOS: Mathematics, products of characters, derived lengths, Mathematics - Group Theory, Mathematics, Arithmetic and combinatorial problems involving abstract finite groups, Conjugacy classes for groups, products of conjugacy classes
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