ON QUASI-REPRESENTING GRAPHS FOR A CLASS OF B(1)-GROUPS

Title & Authors
ON QUASI-REPRESENTING GRAPHS FOR A CLASS OF B(1)-GROUPS
Yom, Peter Dong-Jun;

Abstract
In this article, we give a characterization theorem for a class of corank-1 Butler groups of the form $\small{\mathcal{G}}$($\small{A_1}$, $\small{{\ldots}}$, $\small{A_n}$). In particular, two groups $\small{G}$ and $\small{H}$ are quasi-isomorphic if and only if there is a label-preserving bijection $\small{{\phi}}$ from the edges of $\small{T}$ to the edges of $\small{U}$ such that $\small{S}$ is a circuit in T if and only if $\small{{\phi}(S)}$ is a circuit in $\small{U}$, where $\small{T}$, $\small{U}$ are quasi-representing graphs for $\small{G}$, $\small{H}$ respectively.
Keywords
Butler groups;$\small{\mathcal{B}^{(1)}}$-groups;quasi-representing graphs;quasi-isomorphisms;
Language
English
Cited by
References
1.
D. Arnold and C. Vinsonhaler, Representing graphs for a class of torsion-free abelian groups, Abelian Group Theory (Oberwolfach, 1985), 309-332, Gordon and Breach, New York, 1987.

2.
D. Arnold and C. Vinsonhaler, Quasi-isomorphism invariants for a class of torsion-free abelian groups, Houston J. Math. 15 (1989), no. 3, 327-340.

3.
D. Arnold and C. Vinsonhaler, Invariants for a class of torsion-free abelian groups, Proc. Amer. Math. Soc. 105 (1989), no. 2, 293-300.

4.
D. Arnold and C. Vinsonhaler, Duality and Invariants for Butler groups, Pacific J. Math. 148 (1991), no. 1, 1-9.

5.
F. Richman, An extension of the theory of completely decomposable torsion-free abelian groups, Trans. Amer. Math. Soc. 279 (1983), no. 1, 175-185.

6.
P. Yom, A characterization of a class of Butler groups, Comm. Algebra 25 (1997), no. 12, 3721-3734.

7.
P. Yom, A characterization of a class of Butler groups II, Abelian group theory and related topics (Oberwolfach, 1993), 419-432, Contemp. Math., 171, Amer. Math. Soc., Providence, RI, 1994.

8.
P. Yom, A relationship between vertices and quasi-isomorphism for a class of bracket groups, J. Korean Math. Soc. 44 (2007), no. 6, 1197-1211.