$I$-conjugate operators of an abelian group

Prime Number of Conjugate Operators in a Group.

Perpendicularity in an Abelian Group

We give a set of axioms to establish a perpendicularity relation in anAbelian group and then study the existence of perpendicularities in (Z n , +) and (Q + , ⋅) and in certain other groups. Our approach provides a justification for the use of the symbol⊥ denoting relative primeness in number theory and extends the domain of this convention to some degree. Related to that, we also consider para...

On C0-Group of Linear Operators

In this paper we consider C0-group of unitary operators on a Hilbert C*-module E. In particular we show that if A?L(E) be a C*-algebra including K(E) and ?t a C0-group of *-automorphisms on A, such that there is x?E with =1 and ?t (?x,x) = ?x,x t?R, then there is a C0-group ut of unitaries in L(E) such that ?t(a) = ut a ut*.

Splitting the Automorphism Group of an Abelian P-group

Let G be an abelian p-group sum of finite homocyclic groups Gi. Here, we determine in which cases the automorphism group of G splits over kerσ, where σ :Aut(G) → ∏ iAut(Gi/pGi) is the natural epimorphism. 1. Preliminaries Throghout this paper, p is an arbitrary prime and r is a fixed ordinal number. Let G = ⊕i≤rGi be an abelian p-group, such that Gi is an homocyclic group of exponent pi and fin...

Fuzzy Subgroups of Rank Two Abelian p-Group

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...