### Abstract

Let V be a variety of groups. A group G is said to be almost V-free if every subgroup of G that can be generated by fewer elements than the cardinality of G is contained in a V-free subgroup. It is shown in this paper that if V is a variety in which there is a finite non-abelian simple group, then there are for each positive integer n, 2^{אn } almost V-free groups of cardinality א_{n}.

Original language | English |
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Pages (from-to) | 174-178 |

Number of pages | 5 |

Journal | Journal of Algebra |

Volume | 108 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 1987 |

Externally published | Yes |

## Cite this

Pope, A. L. (1987). Almost-free groups in varieties with torsion.

*Journal of Algebra*,*108*(1), 174-178. https://doi.org/10.1016/0021-8693(87)90130-X