in this paper we illustrate recent results about factorizations of finite groups into conjugate subgroups. the illustrated results are joint works with john cannon, dan levy, attila mar'oti and iulian i. simion.

Let A be a local commutative principal ideal ring. We study the double coset space of GLn(A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A. We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n, k) the dou...

We study the double cosets of a Lie group by a compact Lie subgroup. We show that a Weil formula holds for double coset Lie hypergroups and show that certain representations of the Lie group lift to representations of the double coset Lie hypergroup. We characterize smooth (analytic) vectors of these lifted representations.

In this paper, we construct four infinite families of ternary linear codes associated with double cosets in O(2n+1, q) with respect to certain maximal parabolic subgroup of the special orthogonal group SO(2n + 1, q). Here q is a power of three. Then we obtain two infinite families of recursive formulas , the one generating the power moments of Kloosterman sums with " trace nonzero square argume...

Let H and K be subgroups of a group G. The double cosets of H and K in G are the sets HgK, g E G. In this paper we describe a procedure, P, for determining the cardinality of the set H\G/K of double cosets of H and K in G given a finite presentation for G and finite sets of generators for H and K. It is well known that the problem of determining whether or not a group G defined by a finite pres...

In this paper, we construct an infinite family of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the orthogonal group O(2n+1, q). Here q is a power of two. Then we obtain an infinite family of recursive fomulas generating the odd power moments of Kloosterman sums with trace one arguments in terms of the frequencies of weights in the cod...