The Sym(3) Conjecture and Alt(8)
We give an alternate computer-free proof of a result of Z. Arad, M. Muzychuk, and A. Oliver: if G is a minimal counterexample to the Sym(3) conjecture, then Soc(G)' cannot be isomorphic to Alt(8).
math.GR↗
arXiv subjects
Cecil Andrew Ellard
Publications and source records attributed to Cecil Andrew Ellard.
A Geometric Characterization of Rational Groups
We give a geometric characterization of finite rational groups. In particular, we prove that a finite group is rational if and only if there exists a finite geometry $Γ$ of type $I$ and action of $G$ on $Γ$ as a group of automorphisms such that if $g$ and $h$ are elements of $G$ fixing the same number of flags of type $J$ for all subsets $J$ of $I$, then $g$ and $h$ are conjugate in $G$.
math.GR↗
Rational Groups and a Characterization of a Class of Permutation Groups
We prove that a finite group is rational if and only if it has a set of permutation characters which separate conjugacy classes. It follows from this that a finite group is rational if and only if it has a representation as a permutation group in which any two elements fixing the same number of letters are conjugate.
math.GR↗