ar X iv : 0 71 1 . 28 16 v 1 [ m at h . G R ] 1 8 N ov 2 00 7 Automorphism Groups of Finite p - Groups : Structure and Applications

ar X iv : 0 71 1 . 23 72 v 1 [ m at h . G R ] 1 5 N ov 2 00 7 Braid groups and Artin groups

ar X iv : m at h / 06 02 50 8 v 2 [ m at h . G R ] 1 9 N ov 2 00 7 PRESENTATIONS OF FINITE SIMPLE GROUPS : A QUANTITATIVE APPROACH

There is a constant C 0 such that all nonabelian finite simple groups of rank n over Fq, with the possible exception of the Ree groups 2 G 2 (3 2e+1), have presentations with at most C 0 generators and relations and total length at most C 0 (log n + log q). As a corollary, we deduce a conjecture of Holt: there is a constant C such that dim H 2 (G, M) ≤ C dim M for every finite simple group G, e...

ar X iv : 0 71 1 . 27 39 v 1 [ m at h . N T ] 1 9 N ov 2 00 7 ASYMPTOTIC COHOMOLOGY OF CIRCULAR UNITS

— Let F be a number field, abelian over Q, and fix a prime p 6= 2. Consider the cyclotomic Zp-extension F∞/F and denote Fn the n th finite subfield and Cn its group of circular units. Then the Galois groups Gm,n = Gal(Fm/Fn) act naturally on the Cm’s (for any m ≥ n >> 0). We compute the Tate cohomology groups Ĥ(Gm,n, Cm) for i = −1, 0 without assuming anything else neither on F nor on p.

ar X iv : h ep - p h / 00 11 11 7 v 1 8 N ov 2 00 0 1 ( Mis ) Understanding the Atmospheric Neutrino Anomaly

ar X iv : 0 71 1 . 28 49 v 1 [ m at h . C O ] 1 9 N ov 2 00 7 Partitioning complete graphs by heterochromatic trees ∗

A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an r-edge-colored graph G, denoted by tr(G), is the minimum positive integer p such that whenever the edges of the graph G are colored with r colors, the vertices of G can be covered by at most p vertex-disjoint heterochromatic trees. In this paper we determi...