For a finite group G, subgroup P of G is 2-minimal if B<P, where B=NG(S) for some Sylow 2-subgroup S and B contained in unique maximal P. Here we give detailed explicit description all the subgroups symplectic groups defined over field odd characteristic.

in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

Based on the ideas in some recently uncovered notes of Selberg [14] on discrete subgroups of a product of SL2(R)’s, we show that a discrete subgroup of SL3(R) generated by lattices in upper and lower triangular subgroups is an arithmetic subgroup and hence a lattice in SL3(R).

The lager brewing yeasts, Saccharomyces pastorianus (synonym Saccharomyces carlsbergensis), are allopolyploid, containing parts of two divergent genomes. Saccharomyces cerevisiae contributed to the formation of these hybrids, although the identity of the other species is still unclear. The presence of alleles specific to S. cerevisiae and S. pastorianus was tested for by PCR/RFLP in brewing yea...

We prove that the subgroups of the Thompson group V which are closed under a binary operation introduced by K. S. Brown are in bijective correspondence with a class of varieties of algebras with a single binary operation. In addition, we prove that there are exactly three such proper subgroups which contain the Thompson group F . 2000 AMS Subject Classification: 20F05, 20M18.

Dollar spot, caused by Sclerotinia homoeocarpa, is the most prevalent and economically important turfgrass disease in North America. Increasing levels of fungicide resistance, coupled with tightening environmental scrutiny of existing fungicides, has left fewer options for managing dollar spot. More knowledge about S. homoeocarpa populations is needed to improve dollar spot management strategie...

A p-local finite group consists of a finite p-group S, together with a pair of categories which encode “conjugacy” relations among subgroups of S, and which are modelled on the fusion in a Sylow p-subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as p-completed classifying spaces of finite groups. In this paper, we exa...

Now let G be a group with a finite symmetric generating set S. For any subgroup Gi of G, let X(G/Gi;S) be the Schreier coset graph of G/Gi with respect to S. Then G is said to have Property τ with respect to a collection of finite index subgroups {Gi} if infi h(X(G/Gi ;S)) > 0. This turns out not to depend on the choice of finite generating set S. Also, G is said to have Property τ if it has Pr...