6533b82bfe1ef96bd128cf20
RESEARCH PRODUCT
Groups described by element numbers
Hermann HeinekenFrancesco G. Russosubject
Pure mathematics$p$-groupApplied MathematicsGeneral MathematicsFrobenius group$\mathcal{Q}$-groupssymbols.namesakeSettore MAT/02 - AlgebrasymbolsExponentexponentElement (category theory)MathematicsFrobenius theorem (real division algebras)description
Abstract Let G be a finite group and L e ( G ) = { x ∈ G ∣ x e = 1 } $L_e(G)=\lbrace x \in G \mid x^e=1\rbrace $ , where e is a positive integer dividing | G | $\vert G\vert $ . How do bounds on | L e ( G ) | $\vert L_e(G)\vert $ influence the structure of G? Meng and Shi [Arch. Math. (Basel) 96 (2011), 109–114] have answered this question for | L e ( G ) | ≤ 2 e $\vert L_e(G)\vert \le 2e$ . We generalize their contributions, considering the inequality | L e ( G ) | ≤ e 2 $\vert L_e(G)\vert \le e^2$ and finding a new class of groups of whose we study the structural properties.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-07-05 |