Displaying 241 – 260 of 1355

Showing per page

Endomorphism kernel property for finite groups

Heghine Ghumashyan, Jaroslav Guričan (2022)

Mathematica Bohemica

A group G has the endomorphism kernel property (EKP) if every congruence relation θ on G is the kernel of an endomorphism on G . In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian groups which have EKP.

Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics

Tatiana Bandman, Shelly Garion, Boris Kunyavskiĭ (2014)

Open Mathematics

We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.

Equivalent conditions for p-nilpotence

Keresztély Corrádi, Erzsébet Horváth (2000)

Discussiones Mathematicae - General Algebra and Applications

In the first part of this paper we prove without using the transfer or characters the equivalence of some conditions, each of which would imply p-nilpotence of a finite group G. The implication of p-nilpotence also can be deduced without the transfer or characters if the group is p-constrained. For p-constrained groups we also prove an equivalent condition so that O q ' ( G ) P should be p-nilpotent. We show an example that this result is not true for some non-p-constrained groups. In the second part of the...

Currently displaying 241 – 260 of 1355