Strange divisibility in groups and rings

Autor:	Klyachko, Anton A., Mkrtchyan, Anna A.
Rok vydání:	2015
Předmět:	Mathematics - Group Theory Mathematics - Rings and Algebras
Zdroj:	Archiv der Mathematik, 108:5 (2017), 441-451
Druh dokumentu:	Working Paper
DOI:	10.1007/s00013-016-1008-x
Popis:	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. Comment: 7 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V.2: misprints corrected, some applications generalised. V.3: minor additions and corrections. V.4: Some corrections and generalisations (see Theorem on Monomorphisms and Subgroups). V.5: A reference is added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1506.08967 Zobrazit plný text záznamu View this record from Arxiv