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Finite groups with some restriction on the vanishing set. (English) Zbl 07253635
Summary: Let $$x$$ be an element of a finite group $$G$$ and denote the order of $$x$$ by $$\text{ord}(x).$$ We consider a finite group $$G$$ such that $$\text{gcd(ord}(x), \text{ord}(y)) \leqslant 2$$ 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.

##### MSC:
 20C15 Ordinary representations and characters
GAP
Full Text:
##### References:
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