In practice the hypothesis that x(uv) # ~(u’v) for some conjugate U’ of u is almost always satisfied. When x is faithful and u = v-r, then this just asserts that u does not belong to the center of G (though it is an easy exercise to give a direct proof of the theorem in this case). We shall derive Theorem 1 from a general result (Theorem 2) about common constituents of permutation characters. T...

The centralizer algebra of the action of U(n) on the real tensor powers ⊗RV of its natural module, V = Cn, is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with the invariants for U(n) and with the decomposition of ⊗RV into irreducible submodules is considered.

Abstract For any infinite transitive sofic shift X we construct a reversible cellular automaton (that is, an automorphism of the ) which breaks given finite point subshift into collection gliders traveling opposing directions. This shows in addition that every has is sensitive with respect to all As another application prove finitary version Ryan’s theorem: group $\operatorname {\mathrm {Aut}}(...

‎Let $R$ be a ring with involution $*$‎. ‎An additive mapping $T:Rto R$ is called a left(respectively right) centralizer if $T(xy)=T(x)y$ (respectively $T(xy)=xT(y)$) for all $x,yin R$‎. ‎The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.