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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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##### References:
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