Let S be a semigroup. The elements a, b ∈ S are called primarily conjugate if a = xy and b = yx for certain x, y ∈ S. The relation of conjugacy is defined as the transitive closure of the relation of primary conjugacy. In the case when S is a monoid, denote by G the group of units of S. Then the relation of G-conjugacy is defined by a ∼G b ⇐⇒ a = gbg for certain g ∈ G. We establish the structur...

We consider several computational problems related to conjugacy between subshifts of finite type, restricted k -block codes: verifying a proposed conjugacy, deciding if two shifts admit and reducing the representation size shift via conjugacy. give polynomial-time algorithm for verification, show GI - NP -hardness size, respectively. Our approach focuses on 1-block conjugacies vertex shifts, fr...

This article is concerned with conjugacy problems arising in homeomorphisms group, Hom(F ), of non-compact subsets F of normed vector spaces E. Given two homeomorphisms f and g in Hom(F ), it is shown how the existence of a conjugacy may be related to the existence of a common generalized eigenfunction of the associated Koopman operators. This common eigenfunction serves to build a topology on ...

We show that for every effective left conjugacy closed left quasigroup, there is an induced rack that retains the conjugation structure of the left translations. This means that cryptographic protocols relying on conjugacy search can be secure only if conjugacy search of left translations is infeasible in the induced rack. We note that, in fact, protocols based on conjugacy search could be simp...

Let G be a quasi-split connected reductive group over a local field of characteristic 0, and fix a regular nilpotent element in the Lie algebra g of G. A theorem of Kostant then provides a canonical conjugacy class within each stable conjugacy class of regular semisimple elements in g. Normalized transfer factors take the value 1 on these canonical conjugacy classes.

We classify the real and strongly real conjugacy classes in PGLnðqÞ, PSLnðqÞ, and all quasi-simple covers of PSLnðqÞ. In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. This is a companion paper to [4] in which we classified the real and strongly real conjugacy classes in GLnðqÞ and SLnðqÞ.

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.

We classify the real and strongly real conjugacy classes in PGLnðqÞ, PSLnðqÞ, and all quasi-simple covers of PSLnðqÞ. In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. This is a companion paper to [4] in which we classified the real and strongly real conjugacy classes in GLnðqÞ and SLnðqÞ.