Automorphisms of finite groups of bounded rank

1993 ◽  
Vol 82 (1-3) ◽  
pp. 395-404 ◽  
Author(s):  
Aner Shalev
Keyword(s):  
Finite Groups ◽  
Bounded Rank

scholarly journals On finite groups whose derived subgroup has bounded rank

2010 ◽  
Vol 178 (1) ◽  
pp. 51-60 ◽  
Author(s):  
K. Podoski ◽  
B. Szegedy
Keyword(s):  
Finite Groups ◽  
Derived Subgroup ◽  
Bounded Rank

AN APPROACH TO CAPABLE GROUPS AND SCHUR’S THEOREM

2015 ◽  
Vol 92 (1) ◽  
pp. 52-56
Author(s):  
MITRA HASSANZADEH ◽  
RASOUL HATAMIAN
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Finiteness Condition ◽  
Schur’S Theorem ◽  
Derived Subgroup ◽  
Capable Groups ◽  
A Finite Group ◽  
Bounded Rank

Podoski and Szegedy [‘On finite groups whose derived subgroup has bounded rank’, Israel J. Math.178 (2010), 51–60] proved that for a finite group $G$ with rank $r$, the inequality $[G:Z_{2}(G)]\leq |G^{\prime }|^{2r}$ holds. In this paper we omit the finiteness condition on $G$ and show that groups with finite derived subgroup satisfy the same inequality. We also construct an $n$-capable group which is not $(n+1)$-capable for every $n\in \mathbf{N}$.

scholarly journals FINITE GROUPS WITH ENGEL SINKS OF BOUNDED RANK

2018 ◽  
Vol 60 (3) ◽  
pp. 695-701 ◽  
Author(s):  
E. I. KHUKHRO ◽  
P. SHUMYATSKY
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Finite Groups ◽  
A Finite Group ◽  
Bounded Rank

AbstractFor an element g of a group G, an Engel sink is a subset ${\mathscr E}$(g) such that for every x ∈ G all sufficiently long commutators [. . .[[x, g], g], . . ., g] belong to ${\mathscr E}$(g). A finite group is nilpotent if and only if every element has a trivial Engel sink. We prove that if in a finite group G every element has an Engel sink generating a subgroup of rank r, then G has a normal subgroup N of rank bounded in terms of r such that G/N is nilpotent.

Enumeration of Finite Groups

2007 ◽  
Author(s):  
Simon R. Blackburn ◽  
Peter M. Neumann ◽  
Geetha Venkataraman
Keyword(s):  
Finite Groups
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