Let $G$ be a finite group and $L_e(G)=\{x \in G \ | \ x^e=1\}$, where $e$ is a positive integer dividing $|G|$. How do bounds on $|L_e(G)|$ influence the structure of $G$ ? Meng and Shi [W. Meng and J. Shi, On an inverse problem of Frobenius' theorem, Arch. Math. (Basel) 96 (2011), 109--114] have answered this question for $|L_e(G)| \le 2e$. We generalize their contributions, considering the inequality $|L_e(G)| \le e^2$ and finding a new class of groups of whose we study the structural properties.
Heineken, H., Russo, F. (2013). Groups described by element numbers. FORUM MATHEMATICUM, in stampa.
Groups described by element numbers
RUSSO, Francesco
2013-01-01
Abstract
Let $G$ be a finite group and $L_e(G)=\{x \in G \ | \ x^e=1\}$, where $e$ is a positive integer dividing $|G|$. How do bounds on $|L_e(G)|$ influence the structure of $G$ ? Meng and Shi [W. Meng and J. Shi, On an inverse problem of Frobenius' theorem, Arch. Math. (Basel) 96 (2011), 109--114] have answered this question for $|L_e(G)| \le 2e$. We generalize their contributions, considering the inequality $|L_e(G)| \le e^2$ and finding a new class of groups of whose we study the structural properties.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
