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On the critical group of the \(n\)-cube. (English) Zbl 1023.05096
Summary: Reiner proposed two conjectures about the structure of the critical group of the \(n\)-cube \(Q_n\). In this paper we confirm them. Furthermore we describe its \(p\)-primary structure for all odd primes \(p\). The results are generalized to Cartesian products of complete graphs \(K_{n_1}\times\cdots\times K_{n_k}\) by Jacobson, Niedermaier and Reiner.

MSC:
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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