On Hurwitz generation and genus actions of sporadic groups
نویسندگان
چکیده
منابع مشابه
On the multiplicity-free actions of the sporadic simple groups
We introduce a database containing the character tables of the endomorphism rings of the multiplicity-free permutation modules of the sporadic simple groups, their automorphism groups, their Schur covers, and their bicyclic extensions. We describe the techniques used to compile the data, and present a couple of applications to orbital graphs. MSC: 20C34, 20C40, 20B25, 20B40, 20D08, 05C25.
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 $f$ 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 کاملAn update on Hurwitz groups
A Hurwitz group is any non-trivial finite quotient of the (2, 3, 7) triangle group, that is, any non-trivial finite group generated by elements x and y satisfying x2 = y3 = (xy)7 = 1. Every such group G is the conformal automorphism group of some compact Riemann surface of genus g > 1, with the property that |G| = 84(g − 1), which is the maximum possible order for given genus g. This paper prov...
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: Illinois Journal of Mathematics
سال: 1989
ISSN: 0019-2082
DOI: 10.1215/ijm/1255988653