Consuelo Martínez

Graded simple Jordan superalgebras of growth one

Introduction Structure of the even part Cartan type Even part is direct sum of two loop algebras

Lie superalgebras graded by P(n) and Q(n)

A

Specializations of Jordan Superalgebras

is a loop algebra

Weak Keys in MST1

J

On power subgroups of profinite groups

is a finite dimensional Jordan superalgebra or a Jordan superalgebra of a superform The main case Impossible cases Bibliography.

Representation theory of Jordan superalgebras I

In this article we study Lie superalgebras graded by the root systems P (n) and Q(n).

COORDINATE SETS OF GENERALIZED GALOIS RINGS

Construimos algebras envolventes universales asociativas para varias superalgebras de Jordan.

Classification of bernstein algebras of type (3, n - 3)

The public key cryptosystem MST1 has been introduced by Magliveras et al. [12] (Public Key Cryptosystems from Group Factorizations. Jatra Mountain Mathematical Publications). Its security relies on the hardness of factoring with respect to wild logarithmic signatures. To identify ‘wild-like’ logarithmic signatures, the criterion of being totally-non-transversal has been proposed. We present tame totally-non-transversal logarithmic signatures for the alternating and symmetric groups of degree ≥ 5. Hence, basing a key generation procedure on the assumption that totally-non-transversal logarithmic signatures are ‘wild like’ seems critical. We also discuss the problem of recognizing ‘weak’ totally-non-transversal logarithmic signatures, and demonstrate that another proposed key generation procedure based on permutably transversal logarithmic signatures may produce weak keys.

Unital bimodules over the simple Jordan superalgebra

In this paper we prove that if G is a finitely generated pro-(finite nilpotent) group, then every subgroup Gn , generated by nth powers of elements of G, is closed in G. It is also obtained, as a consequence of the above proof, that if G is a nilpotent group generated by m elements xl, ... , xm, then there is a function f(m, n) such that if every word in x?l of length 1, we denote the subgroups of G generated by all nth powers an, a E G. A. Shalev conjectured that for any n the subgroup Gn is closed in G. This is the same as saying that for arbitrary integers m > 1, n > 1 there exists an integer N = N(m, n) such that in an arbitrary m-generated finite group G every product of nth powers of elements of G can be represented in the form a, **N where ai E G, 1 < i < N. Let us show, for example, that the existence of a function N(m, n) implies that Gn is closed. The subset M = {an . . *aN: al, ... , aN E G} of G is closed as the image of the compact G x ... x G under the continuous map (al, ., aN) -a an ... an Now we can consider the finite nilpotent group G/H, where H is an arbitrary open subgroup of G and so we have GnH = MH, which implies that Gn lies in the closure of M. Hence Gn = M. In this paper we prove Shalevs Conjecture when G is a pro-(finite nilpotent) Received by the editors February 8, 1994. 1991 Mathematics Subject Classification. Primary 20E18; Secondary 20F05. ? 1994 American Mathematical Society 0002-9947/94

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