it is proved here that if $g$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble, then $g$ is either locally supersoluble or a vcernikov group. the same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups. as a consequence, it is shown that any infinite locally graded gro...

We construct an example of conjugacy separable group possessing a not conjugacy separable subgroup of finite index. We give also a sufficient condition for a conjugacy separable group to preserve this property when passing to subgroups of finite index. We establish also conjugacy separability of finitely presented residually free groups using impressive results of Bridson and Wilton [BW-07].

a finite group $g$ satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes $m$ and $n$ are either equal or have a common divisor a prime power. taeri conjectured that an insoluble group satisfying this condition is isomorphic to $s times a$ where $a$ is abelian and $s cong psl_2(q)$ for $q in {4,8}$. we confirm this conjecture.

Conjugate gradient methods are a class of important methods for unconstrained optimization, especially when the dimension is large. This paper proposes a new conjugacy condition, which considers an inexact line search scheme but reduces to the old one if the line search is exact. Based on the new conjugacy condition, two nonlinear conjugate gradient methods are constructed. Convergence analysis...

We provide a complete classification up to conjugacy of the binary shifts of finite commutant index on the hyperfinite II(1), factor. There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.

We provide a complete classification up to conjugacy of the binary shifts of commutant index 2 on the hyperfinite II(1) factor. There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.

A graph product is the fundamental group of a graph of groups Amongst the simplest examples are HNN groups and free products with amalgamation. The conjugacy problem is solvable for recursively presented graph products with cyclic edge groups over finite graphs if the vertex groups have solvable conjugacy problem and the sets of cyclic generators in them are semicritical. For graph products ove...

We show that untwisted respectively twisted conjugacy classes of a compact and simply connected Lie group which satisfy a certain integrality condition correspond naturally to irreducible highest weight representations of the corresponding affine Lie algebra. Along the way, we review the classification of twisted conjugacy classes of a simply connected compact Lie group G and give a description...