J. Korean Math. Soc. 2012; 49(3): 493-502
Printed May 1, 2012
https://doi.org/10.4134/JKMS.2012.49.3.493
Copyright © The Korean Mathematical Society.
Peter Dongjun Yom
Bronx Community College of CUNY
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
2007; 44(6): 1197-1211
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