A conjugacy class C of a finite group G is a sign conjugacy class if every irreducible character of G takes value 0, 1 or −1 on C. In this paper we classify the sign conjugacy classes of the symmetric groups and thereby verify a conjecture of Olsson.

Let G be a connected reductive algebraic group defined over a field k of characteristic not 2, θ an involution of G defined over k, H a k-open subgroup of the fixed point group of θ and Gk (resp. Hk) the set of k-rational points of G (resp. H). The variety Gk/Hk is called a symmetric k-variety. For real and -adic symmetric k-varieties the space L(Gk/Hk ) of square integrable functions decompose...

For every finitely generated recursively presented group G we construct a finitely presented group H containing G such that G is (Frattini) embedded into H and the group H has solvable conjugacy problem if and only if G has solvable conjugacy problem. Moreover G and H have the same r.e. Turing degrees of the conjugacy problem. This solves a problem by D. Collins.

A nonlinear conjugate gradient algorithm which is a modification of the Dai and Yuan [Y.H. Dai and Y, Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10 (1999), pp.177-182.] conjugate gradient algorithm satisfying a parametrized sufficient descent condition with a parameter k δ is proposed. The parameter k δ is computed by means of the conj...

LetM be a closed, orientable, irreducible, geometrizable 3-manifold. We prove that the profinite topology on the fundamental group of π1(M) is efficient with respect to the JSJ decomposition of M . We go on to prove that π1(M) is good, in the sense of Serre, if all the pieces of the JSJ decomposition are. We also prove that if M is a graph manifold then π1(M) is conjugacy separable. A group G i...

We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced and developed in the past few years. We will see how the properties of these graphs, along with some ex...

In this paper we prove that a free product of conjugacy separable groups A and B, amalgamating a cyclic subgroup, is conjugacy separable if A and B are subgroup separable, cyclic conjugacy separable, 2-free, and residually p-finite, for all prime numbers p. The following result is an example of the applications we obtain as consequences of our main theorem. Let A and B each be a free product of...

(A) We study in this paper topological properties of conjugacy classes in Polish groups. There are two questions which we are particularly interested in. First, does a Polish group G have a dense conjugacy class? This is equivalent (see, e.g., Kechris [95, 8.47]) to the following generic ergodicity property of G: Every conjugacy invariant subset A ⊆ G with the Baire property (e.g., a Borel set)...

By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. We conjecture that this measure agrees with a second measure on conjugacy classes of the Weyl group induced by a construction o...

The conjugacy problem and the inverse conjugacy problem of a finitely generated group are defined, from a language theoretic point of view, as sets of pairs of words. An automaton might be obliged to read the two input words synchronously, or could have the option to read asynchronously. Hence each class of languages gives rise to four classes of groups; groups whose (inverse) conjugacy problem...