Small torsion generating sets for hyperelliptic mapping class groups

Generating Mapping Class Groups by Involutions

Let Σg,b denote a closed oriented surface genus g with b punctures and let Modg,b denote its mapping class group. In [10] Luo proved that if the genus is at least 3, the group Modg,b is generated by involutions. He also asked if there exists a universal upper bound, independent of genus and the number of punctures, for the number of torsion elements/involutions needed to generate Modg,b. Brendl...

The Zieschang-McCool method for generating algebraic mapping-class groups

Let g, p ∈ [0↑∞ [, the set of non-negative integers. Let Ag,p denote the group consisting of all those automorphisms of the free group on t[1↑p]∪x[1↑g]∪y[1↑g] which fix the element Π j∈[p↓1] tj Π i∈[1↑g] [xi, yi] and permute the set of conjugacy classes { [tj ] : j ∈ [1↑p]}. Labruère and Paris, building on work of Artin, Magnus, Dehn, Nielsen, Lickorish, Zieschang, Birman, Humphries, and others...

K - theory of mapping class groups III : Odd torsion Luke

Bounds for the `-torsion in Class Groups

We prove for each integer ` ≥ 1 an unconditional upper bound for the size of the `-torsion subgroup ClK [`] of the class group of K, which holds for all but a zero density set of number fields K of degree d ∈ {4, 5} (with the additional restriction in the case d = 4 that the field be non-D4). For sufficiently large ` this improves recent results of Ellenberg, Matchett Wood, and Pierce, and is a...

Generating Sets of Mathieu Groups

Julius Whiston [6] calculated the maximum size of an irredundant generating set for Sn and An by examination of maximal subgroups. Using analogous considerations, we will compute upper bounds to this value for the first two Mathieu groups, M11 and M12. Computational results gave explicit irredundant generating sets of M11 and M12 of size 5 and 6, respectively. Together these give the full resul...