The group K2 of a curve C over a finite field is equal to the tame kernel of the corresponding function field. We describe two algorithms for computing generators of the tame kernel of a global function field. The first algorithm uses the transfer map and the fact that the `-torsion can easily be described if the ground field contains the `th roots of unity. The second method is inspired by an ...

The Diffie-Hellman key agreement protocol is based on taking large powers of a generator of a prime-order cyclic group. Some generators allow faster exponentiation. We show that to a large extent, using the fast generators is as secure as using a randomly chosen generator. On the other hand, we show that if there is some case in which fast generators are less secure, then this could be used by ...

We list the subgroups of the basis set of Cl3,0 and classify them according to three criteria for construction of universal Clifford algebras: (1) each generator squares to ±1, (2) the generators within the group anticommute, and (3) the order of the resulting group is 2, where n is the number of nontrivial generators. Obedient groups we call choirs; disobedient groups, bands. We classify choir...

After 100 years of effort, the classification of all the finite subgroups of SU(3) is yet incomplete. The most recently updated list can be found in [3], where the structure of the series (C) and (D) of SU(3)-subgroups is studied. We provide a minimal set of generators for one of these groups which has order 162. These generators appear up to phase as the image of an irreducible unitary braid g...

Modern power systems are a very complex dynamical system spreading over a large geographical area. They indicate very complex phenomena in some parts as well as in the whole interconnected power system. In large and complex systems, there are coherent groups of generators. A group of generators in one area swings against a group of generators in another area. In this paper, using the Huang's Em...

of the Dissertation Finite generators for countable group actions; Finite index pairs of equivalence relations; Complexity measures for recursive programs

We study the ratio ergodic theorem (RET) of Hopf for group actions. Under a certain technical condition, if a sequence of sets {Fn} in a group satisfy the RET, then there is a finite set E such that {EFn} satisfies the Besicovitch covering property. Consequently for the abelian group G = ⊕n=1Z there is no sequence Fn ⊆ G along which the RET holds, and in many finitely generated groups, includin...

We exhibit an implementation in the computeralgebra system GAP of a method to approximate generators of an integral arithemtic group.

‎let $i$ be an ideal in a regular local ring $(r,n)$‎, ‎we will find‎ ‎bounds on the first and the last betti numbers of‎ ‎$(a,m)=(r/i,n/i)$‎. ‎if $a$ is an artinian ring of the embedding‎ ‎codimension $h$‎, ‎$i$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $a$ a {it $t-$extended stretched local ring}‎. ‎this class of‎ ‎local rings is a natural generalization of the class of stretched ...