Hurwitz generation in groups of types
نویسندگان
چکیده
Abstract A Hurwitz generating triple for a group
منابع مشابه
finite simple groups of low rank: hurwitz generation and $(2,3)$-generation
let us consider the set of non-abelian finite simple groups which admit non-trivial irreducible projective representations of degree $le 7$ over an algebraically closed field $f$ of characteristic $pgeq 0$. we survey some recent results which lead to the complete list of the groups in this set which are $(2, 3, 7)$-generated and of those which are $(2,3)$-generated.
متن کاملfinite simple groups of low rank: hurwitz generation and (2,3)-generation
let us consider the set of non-abelian finite simple groups which admit non-trivial irreducible projective representations of degree $le 7$ over an algebraically closed field $mathbb{f}$ of characteristic $pgeq 0$. we survey some recent results which lead to the complete list of the groups in this set which are $(2,3,7)$-generated and of those which are $(2,3)$-generated.
متن کاملHurwitz Groups and Surfaces
Hurwitz not only gave an upper bound for the number of automorphisms of a compact Riemann surface of genus greater than 2, but also gave a characterization of which finite groups could be groups of automorphisms achieving this bound. In practice, however, the identification of such groups and of the surfaces they act on is difficult except in special cases. We survey what is known. 1. How I Got...
متن کاملHurwitz Equivalence in Dihedral Groups
In this paper we determine the orbits of the braid group Bn action on Gn when G is a dihedral group and for any T ∈ Gn. We prove that the following invariants serve as necessary and sufficient conditions for Hurwitz equivalence. They are: the product of its entries, the subgroup generated by its entries, and the number of times each conjugacy class (in the subgroup generated by its entries) is ...
متن کاملp-adic Hurwitz groups
Herrlich showed that a Mumford curve of genus g > 1 over the p-adic complex field Cp has at most 48(g− 1), 24(g− 1), 30(g− 1) or 12(g− 1) automorphisms as p = 2, 3, 5 or p > 5. The Mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p-adic triangle groups ∆p for p ≤ 5, or in a p-adic quadrangle group p for p > 5. The finite groups attaining these...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2022
ISSN: ['1435-4446', '1433-5883']
DOI: https://doi.org/10.1515/jgth-2021-0115