A GAP package for braid orbit computation, and applications

Let G be a finite group. By Riemann's Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy group G. Thus many problems on algebraic curves require the computation of braid orbits. In this paper we describe an implementation of this computation. We discuss several applications, including the classification of irreducible families of indecomposable rational functions with exceptional monodromy group

Rank 3 permutation characters and maximal subgroups

In this paper we classify all maximal subgroups M of a nearly simple primitive rank 3 group G of type L=Omega_{2m+1}(3), m > 3; acting on an L-orbit E of non-singular points of the natural module for L such that 1_P^G <=1_M^G where P is a stabilizer of a point in E. This result has an application to the study of minimal genera of algebraic curves which admit group actions.Comment: 41 pages, to appear in Forum Mathematicu

Alternating groups and moduli space lifting Invariants

Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves Fried-Serre on deciding when sphere covers with odd-order branching lift to unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp. odd) theta functions when r is even (resp. odd). For inner spaces the result is independent of r. Another use appears in, http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for the prime p=2 lying over Hurwitz spaces first studied by, http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*) High tower levels are general-type varieties and have no rational points.For infinitely many of those MTs, the tree of cusps contains a subtree -- a spire -- isomorphic to the tree of cusps on a modular curve tower. This makes plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs. Establishing these modular curve-like properties opens, to MTs, modular curve-like thinking where modular curves have never gone before. A fuller html description of this paper is at http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from proof sheets, but does include some proof simplification in \S

Embeddings in Non-Vacuum Spacetimes

A scheme is discussed for embedding n-dimensional, Riemannian manifolds in an (n+1)-dimensional Einstein space. Criteria for embedding a given manifold in a spacetime that represents a solution to Einstein's equations sourced by a massless scalar field are also discussed. The embedding procedures are illustrated with a number of examples.Comment: 17 pages, Plain Latex. Extended discussion on embeddings with scalar fields and further examples included. In press, Classical and Quantum Gravit

On Applications of Campbell's Embedding Theorem

A little known theorem due to Campbell is employed to establish the local embedding of a wide class of 4-dimensional spacetimes in 5-dimensional Ricci-flat spaces. An embedding for the class of n-dimensional Einstein spaces is also found. The local nature of Campbell's theorem is highlighted by studying the embedding of some lower-dimensional spaces.Comment: 17 pages, standard Latex sourc

Black box exceptional groups of Lie type

If a black box group is known to be isomorphic to an exceptional simple group of Lie type of (twisted) rank &gt; 1 &gt;1 , other than any 2 F 4 ( q ) ^2\kern -.8pt F_4(q) , over a field of known size, a Las Vegas algorithm is given to produce a constructive isomorphism. In view of its timing, this algorithm yields an upgrade of all known nearly linear time Monte Carlo permutation group algorithms to Las Vegas algorithms when the input group has no composition factor isomorphic to any group 2 F 4 ( q ) ^2\kern -.8pt F_4(q) or 2 G 2 ( q ) ^2G_2(q) .</p

Generation of finite quasisimple groups with an application to groups acting on Beauville surfaces

We verify a conjecture of Bauer Catanese and Grunewald by proving a stronger result concerning quasisimple groups. More specifically, we prove that every finite quasisimple group apart from A5 and its cover SL(2,5) is a Beauville group