Journal of the
Korean Mathematical Society JKMS

In this article, we give a characterization theorem for a class of corank--1 Butler groups of the form $\mathcal{G}(A_1,\ldots,A_n)$. In particular, two groups $G$ and $H$ are quasi-isomorphic if and only if there is a label-preserving bijection $\phi$ from the edges of $T$ to the edges of $U$ such that $S$ is a circuit in $T$ if and only if $\phi(S)$ is a circuit in $U$, where $T,U$ are quasi-representing graphs for $G,H$ respectively.

Keywords: Butler groups, $\mathcal{B}^{(1)}$-groups, quasi-representing graphs, quasi-isomorphisms

MSC numbers: Primary 20K15