Related papers: Generating the Level 2 Subgroup by Involutions
We show that any group $G$ is contained in some sharply 2-transitive group $\mathcal{G}$ without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups $\mathcal{G}$ that we…
We give an infinite presentation for the mapping class group of a non-orientable surface with boundary components. The presentation is a generalization of the presentation given by the second author [15].
In this paper we give a classification of classes of involutions on an automorphism group of an octonion algebra over fields of characteristic 2, and describe the classes of their fixed point groups.
Consider the special linear group of degree $2$ over an arbitrary finite field, acting on the full space of $2 \times 2$-matrices by transpose. We explicitly construct a generating set for the corresponding modular matrix invariant ring,…
We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most $2n+1$ ends, and with symmetry…
We compute the invariant subspace of the rational group ring of a surface, truncated by powers of the augmentation ideal, under the action of the mapping class group. The surface is compact, oriented with one boundary component. This…
A subset $S$ of a group $G$ invariably generates $G$ if, when each element of $S$ is replaced by an arbitrary conjugate, the resulting set generates $G.$ An invariable generating set $X$ of $G$ is called minimal if no proper subset of $X$…
We focus on two kinds of infinite index subgroups of the mapping class group of a surface associated with a Lagrangian submodule of the first homology of a surface. These subgroups, called Lagrangian mapping class groups, are known to play…
We show that the decomposition group of a line $L$ in the plane, i.e. the subgroup of plane birational transformations that send $L$ to itself birationally, is generated by its elements of degree 1 and one element of degree 2, and that it…
We give Dehn twist--crosscap slide presentations for involutions on non-orientable surfaces of genera up to 5.
We classify the minimal algebraic surfaces of general type with $p_g=q=1, K^2=8$ and bicanonical map of degree 2. It will turn out that they are isogenous to a product of curves, so that if $S$ is such a surface then there exist two smooth…
This paper is the first part in a 2 part study of an elementary functorial construction from the category of finite non-abelian groups to a category of singular compact, oriented 2-manifolds. After a desingularization process this…
An upper bound on degrees of elements of a minimal generating system for invariants of quivers of dimension (2,...,2) is established over a field of arbitrary characteristic and its precision is estimated. The proof is based on the…
We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an…
We construct inseparable morphisms between curves of genus $\ge 2$ that are degenerations of separable morphisms.
We prove that, except in certain low-complexity cases, the automorphism group of the graph of pants decompositions of a nonorientable surface is isomorphic to the mapping class group of that surface.
We complete the classification of the finite special linear groups $\SL_n(q)$ which are $(2,3)$-generated, i.e., which are generated by an involution and an element of order $3$. This also gives the classification of the finite simple…
We offer a Maple package SL\_2\_Inv\_Ker for calculating of minimal generating sets for the algebras of joint invariants/semi-invariants of binary forms and for calculations of the kernels of Weitzenb\"ock derivations.
We present two versions of a method for generating all triangulations of any punctured surface in each of these two families: (1) triangulations with inner vertices of degree at least 4 and boundary vertices of degree at least 3 and (2)…
Recently it was shown that a certain class of phylogenetic networks, called level-$2$ networks, cannot be reconstructed from their associated distance matrices. In this paper, we show that they can be reconstructed from their induced…