### Abstract

We prove that every group G of order n has t≤logn/log2 + 0(log log n) elements x_{1},...,x_{1} such that every group element is a product of the form x^{t1}_{ 1}...x^{t1}_{ 1}, e{open} {0.1}. The result is true more generally for quasigroups. As a corollary we obtain that for n even, every one-factorization of the complete graph on n vertices contains at most t one-factors whose union is connected.

Original language | English |
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Pages (from-to) | 27-30 |

Number of pages | 4 |

Journal | North-Holland Mathematics Studies |

Volume | 60 |

Issue number | C |

DOIs | |

Publication status | Published - 1982 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Babai, L., & Erdős, P. (1982). Representation of Group Elements as Short Products.

*North-Holland Mathematics Studies*,*60*(C), 27-30. https://doi.org/10.1016/S0304-0208(08)73487-X