We give a polynomial time algorithm that computes a decomposition of a finite group G given in the form of its multiplication table. That is, given G, the algorithm outputs two subgroups A and B of G such that G is the direct product of A and B, if such a decomposition exists.

A subset X of a group G is called thin if, for every finite F G, there exists H such that Fx∩Fy=∅, xF∩yF=∅ all distinct x,y∈X\H. We prove countable topologizable can be factorized G=AB into subsets A,B.

We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor's results 7]. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application of this procedure is a polynomial quantum Fourier transform algorithm for an arbitrary nite Abelian group. The pape...

We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.

We propose and study two new computational models for quantum computation, and infer new insights about the circumstances that give quantum computers an advantage over classical ones. The bomb query complexity model is a variation on the query complexity model, inspired by the Elitzur-Vaidman bomb tester. In this model after each query to the black box the result is measured, and the algorithm ...

A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...

a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...