Finite groups with some restriction on the vanishing set

Abstract

Let $x$ be an element of a finite group $G$ and denote the order of $x$ by $\mathrm{ord}(x)$. We consider a finite group $G$ such that $\gcd (\mathrm{ord}(x),\mathrm{ord}(y))⩽2$ for any two vanishing elements $x$ and $y$ contained in distinct conjugacy classes. We show that such a group $G$ is solvable. When $G$ with the property above is supersolvable, we show that $G$ has a normal metabelian $2$-complement.

9 pages

References in corpus (1)

• Zeros of primitive characters of finite groups

Cited by in corpus (1)

• On the orders of vanishing elements of finite groups