Let $G$ be a finite group and $L_e(G)=\{x \in G \mid x^e=1\}$, where $e$ is a positive integer dividing $|G|$. How do bounds on $|L_e(G)|$ influence the structure of $G$ ? Meng and Shi [Arch. Math. (Basel) 96 (2011), 109--114] have answered this question for $|L_e(G)| \le 2e$. We generalize their contributions, considering the inequality $|Le(G)| \le e^2$ and finding a new class of groups of whose we study the structural properties.
Groups described by element numbers
Russo F
2015-01-01
Abstract
Let $G$ be a finite group and $L_e(G)=\{x \in G \mid x^e=1\}$, where $e$ is a positive integer dividing $|G|$. How do bounds on $|L_e(G)|$ influence the structure of $G$ ? Meng and Shi [Arch. Math. (Basel) 96 (2011), 109--114] have answered this question for $|L_e(G)| \le 2e$. We generalize their contributions, considering the inequality $|Le(G)| \le e^2$ and finding a new class of groups of whose we study the structural properties.File in questo prodotto:
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