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- W2073634551 abstract "Let q be a power of a prime, and E be an elliptic curve defined over $mathbb{F}_{q}$ . Such curves have a classical group structure, and one can form an infinite tower of groups by considering E over field extensions $mathbb{F}_{q^{k}}$ for all k≥1. The critical group of a graph may be defined as the cokernel of L(G), the Laplacian matrix of G. In this paper, we compare elliptic curve groups with the critical groups of a certain family of graphs. This collection of critical groups also decomposes into towers of subgroups, and we highlight additional comparisons by using the Frobenius map of E over $mathbb{F}_{q}$ ." @default.
- W2073634551 created "2016-06-24" @default.
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- W2073634551 date "2008-11-28" @default.
- W2073634551 modified "2023-09-26" @default.
- W2073634551 title "The critical groups of a family of graphs and elliptic curves over finite fields" @default.
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- W2073634551 doi "https://doi.org/10.1007/s10801-008-0162-z" @default.
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