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arXiv · 1506.08967

Strange divisibility in groups and rings

Anton A. Klyachko·Anna A. Mkrtchyan
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Abstract

We prove a general divisibility theorem that implies, e.g., that, in any group, the number of generating pairs (as well as triples, etc.) is a multiple of the order of the commutator subgroup. Another corollary says that, in any associative ring, the number of Pythagorean triples (as well as four-tuples, etc.) of invertible elements is a multiple of the order of the multiplicative group.

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Anton A. Klyachko, Anna A. Mkrtchyan. 2015-06-30. Strange divisibility in groups and rings. https://doi.org/10.1007/s00013-016-1008-x

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