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...

In this paper we introduce the graph Γsc(G) associated with a group G, called solvable conjugacy class (abbreviated as SCC-graph), whose vertices are nontrivial classes of G and two distinct C,D adjacent if there exist x∈C y∈D such that 〈x,y〉 is solvable. We discuss connectivity, girth, clique number, several other properties SCC-graph. One our results asserts only finitely many finite groups S...

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...

We define a Rohlin property for Z-actions on UHF algebras and show a non-commutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. We consider two classes of UHF algebras. For UHF algebras in one class including the CAR algebra, there is one and only one outer conjugacy class of product type actions and for UHF algebra...

Let G be a finite group, and let Δ(G) the prime graph built on its set of conjugacy class sizes: this is (simple undirected) whose vertices are numbers dividing some size G, two distinct p, q adjacent if only pq divides G. In paper, we characterize structure those groups block square.

We define a Rohlin property for actions of Z on UHF algebras and show a noncommutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. In particular we present two classes of UHF algebras. For UHF algebras in one class, which includes the CAR algebra, there is one and only one outer conjugacy class of product type action...

The known algorithms for solving the conjugacy problem in Garside groups involve computing a particular subset of the conjugacy class, the so-called super summit set. The super summit set [g] of an element g in a Garside group is, intuitively, the set of all conjugates of g that have the shortest normal form in the conjugacy class of g. In this paper, we define the stable super summit set [g] o...

Let G be a finite group, and let Δ(G) the prime graph built on set of conjugacy class sizes G: this is simple undirected whose vertices are numbers dividing some size G, two p q being adjacent if only pq divides G. In present paper, we classify groups for which has cut vertex.

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...