## Abstract

Let A be an infinite set. Denote by Sa the group of all permutations of A, and let R, denote the class of involutions of A moving A elements and fixing i elements (Formula presented) The products R(Rj were determined in [Ml]. In this article we treat the products (Formula presented) Let INF denote the set of permutations in Sa moving infinitely many elements. We show: (Formula presented) contains two integers of different parity; (Formula presented) and all integers in (Formula presented) have the same parity.(Formula presented) satisfies one of the following three conditions: 9 moves precisely three elements. 9 moves precisely five elements. 9 moves precisely seven elements and has order 12. These results were announced in 1973 in [MO]. (1) and part of (2)(a) were generalized recently by Droste [Dl, D2].

Original language | English |
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Pages (from-to) | 462-745 |

Number of pages | 284 |

Journal | Transactions of the American Mathematical Society |

Volume | 307 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1988 |

## ASJC Scopus subject areas

- Mathematics (all)
- Applied Mathematics