1. The dihedral subgroup is non-abelian. If a group G has the property that the squares of its operators constitute a given group then the direct product of G and any abelian group of order 2m and of type (1,1, 1, • • • ) has the same property. Such direct products will always be excluded in what follows. It has been noted that a necessary and sufficient condition that there is at least one gro...

Abstract In this paper, a new upper bound for the Multiple Knapsack Problem (MKP) is proposed, based on idea of relaxing MKP to Bounded Sequential Problem, i.e., multiple knapsack problem in which item sizes are divisible. Such relaxation, called sequential obtained by suitably replacing items instance with divisible sizes. Experimental results benchmark instances show that effective, terms qua...

Divisible E-cash has been introduced twenty years ago but no construction is both fully secure in the standard model and efficiently scalable. In this paper, we fill this gap by providing an anonymous divisible E-cash construction with constant-time withdrawal and spending protocols. Moreover, the deposit protocol is constant-time for the merchant, whatever the spent value is. It just has to co...

In this paper, as homage to Professor Gaspar Mayor in his 70 anniversary, we present a summary of results on BL-algebras and related structures that, using the one-to-one correspondence between divisible finite t-norms and finite BL-chains, allows us to provide an equational characterization of any divisible finite t-norm.

Let F be a (topologically) finitely generated free pro-p-group, and ß an automorphism of F . If p ^ 2 and the order of ß is 2 , then there is some basis of F such that ß either fixes or inverts its elements. If p does not divide the order of ß , then the subgroup of F of all elements fixed by ß is (topologically) infinitely generated; however this is not always the case if p divides the order o...

In the Sylow theorems f we learn that if the order of a group 2Í is divisible hj pa (p a prime integer) and not by jo*+1, then 31 contains one and only one set of conjugate subgroups of order pa, and any subgroup of 21 whose order is a power of p is a subgroup of some member of this set of conjugate subgroups of 2Í. These conjugate subgroups may be called the Sylow subgroups of 21. It will be o...