On the Baer-Lovász-Tutte construction of groups from graphs: isomorphism types and homomorphism notions

Abstract

Let p be an odd prime. From a simple undirected graph G, through the classical procedures of Baer (Trans.

Enumerating conjugacy classes of graphical groups over finite fields

“…It follows that for an odd prime p, H Γ (F p ) is isomorphic to the finite p-group attached to Γ by Li and Qiao [13]. He and Qiao [11,Thm 1.1] showed that for graphs Γ and Γ and an odd prime p, H Γ (F p ) and H Γ (F p ) are isomorphic if and only if Γ and Γ are.…”

Turán and Ramsey problems for alternating multilinear maps

“…of G, including independent sets and vertex colourings [BCG + 20], vertex and edge connectivities [LQ19], and isomorphism and homomorphism notions [HQ20], with properties of φ G . Graph-theoretic questions and techniques have also been translated to study alternating bilinear maps in [LQ17,BCG + 20,Qia20] with applications to group theory and quantun information.…”