0000000000674499
AUTHOR
Hermann Heineken
showing 4 related works from this author
Groups described by element numbers
2013
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.
A Local Approach to Certain Classes of Finite Groups
2003
Abstract We develop several local approaches for the three classes of finite groups: T-groups (normality is a transitive relation) and PT-groups (permutability is a transitive relation) and PST-groups (S-permutability is a transitive relation). Here a subgroup of a finite group G is S-permutable if it permutes with all the Sylow subgroup of G.
THE STRUCTURE OF MUTUALLY PERMUTABLE PRODUCTS OF FINITE NILPOTENT GROUPS
2007
We consider mutually permutable products G = AB of two nilpotent groups. The structure of the Sylow p-subgroups of its nilpotent residual is described.
GENERALIZED HYPERCENTERS IN INFINITE GROUPS
2011
We consider the so-called generalized center, defined by Agrawal, in the slightly wider context of periodic groups and try to find out where additional conditions are needed for refinements. In particular we consider the final terms of the corresponding ascending sequences.