ar X iv : 0 80 8 . 23 81 v 1 [ m at h . G R ] 1 8 A ug 2 00 8 On finite - index extensions of subgroups of free groups ∗

ar X iv : 0 80 8 . 23 81 v 2 [ m at h . G R ] 2 4 Ju l 2 00 9 On finite - index extensions of subgroups of free groups ∗

We study the lattice of finite-index extensions of a given finitely generated subgroup H of a free group F . This lattice is finite and we give a combinatorial characterization of its greatest element, which is the commensurator of H . This characterization leads to a fast algorithm to compute the commensurator, which is based on a standard algorithm from automata theory. We also give a sub-exp...

ar X iv : 0 80 8 . 23 49 v 1 [ m at h . N A ] 1 8 A ug 2 00 8 EULERIAN NUMBERS AND B SPLINES

2000 Mathematics Subject Classification. Primary 65D07; Secondary 11B68.

ar X iv : 0 90 8 . 27 37 v 1 [ m at h . G R ] 1 9 A ug 2 00 9 On Bruck Loops of 2 - power Exponent , II ∗

As anounced in [BSS], we show that the non-passive finite simple groups are among the PSL2(q) with q − 1 ≥ 4 a 2-power.

ar X iv : 0 80 8 . 10 23 v 1 [ qu an t - ph ] 7 A ug 2 00 8 CATEGORICAL QUANTUM MECHANICS

ar X iv : 0 80 8 . 27 24 v 1 [ m at h - ph ] 2 0 A ug 2 00 8 Bosons in Rapid Rotation ∗

Some recent progress in the mathematical physics of rapidly rotating, dilute Bose gases in anharmonic traps is reviewed.