In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup Γ(N), with respect to the usual fundamental domain FN , where N is assumed prime. The cycles Q1, . . . , Qn that this algorithm produces are such that the the corresponding paths γ1, . . . , γn in the Riemann surface X0(N)(C) have a nice behaviour around the elliptic points of...

We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of non-abelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently Hidden Translation in Zp , whenever p is a fixed prime. For the induction step, we introduce the ...

Abstract In this paper, we call a finite group G G an N L M NLM -group ( C NCM -group, respectively) if every non-normal cyclic subgroup of prime order or 4 (prime power order, in is contained maximal . Using the property -groups and -groups, give new necessary suffic...

We show that every weighing matrix of weight n invariant under a finite abelian group G can be generated from a subgroup H of G with |H| ≤ 2n−1. Furthermore, if n is an odd prime power and a proper circulant weighing matrix of weight n and order v exists, then v ≤ 2n−1. We also obtain a lower bound on the weight of group invariant matrices depending on the invariant factors of the underlying

We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of non-abelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently Hidden Translation in Zp , whenever p is a fixed prime. For the induction step, we introduce the ...

If p is an odd prime, then the Gupta-Sidki group Gp is an infinite 2-generated p-group. It is defined in a recursive manner as a particular subgroup of the automorphism group of a regular tree of degree p. In this note, we make two observations concerning the irreducible representations of the group algebra K[Gp] with K an algebraically closed field. First, when charK 6= p, we obtain a lower bo...

It has been shown that there is a Hamilton cycle in every connected Cayley graph on any group G whose commutator subgroup is cyclic of prime-power order. This note considers connected, vertex-transitive graphs X of order at least 3, such that the automorphism group of X contains a vertex-transitive subgroup G whose commutator subgroup is cyclic of prime-power order. We show that of these graphs...

In this paper, we initiate the study of prime bi-ideals (fuzzy bi-ideals) in semirings. We define strongly prime, prime, semiprime, irreducible and strongly irreducible bi-ideals in semirings. We also define strongly prime, semiprime, irreducible, strongly irreducible fuzzy bi-ideals of semirings. We characterize those semirings in which each bi-ideal (fuzzy bi-ideal) is prime (strongly prime).

A unitary strongly prime ring is defined as a prime ring whose central closure is simple with identity element. The class of unitary strongly prime rings is a special class of rings and the corresponding radical is called the unitary strongly prime radical. In this paper we prove some results on unitary strongly prime rings. The results are applied to study the unitary strongly prime radical of...