<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Fernandes, Vítor H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Groups of permutations that are even on maximal proper subsets, and related monoids</style></title></titles><dates><year><style  face="normal" font="default" size="100%">Submitted</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2605.12342</style></url></web-urls></urls><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let n be a positive integer and let [n]={1,2,…,n}. Let Γ_n denote the group of permutations on [n] whose restrictions to maximal proper subsets of [n] are even, let Σ_n denote the monoid of transformations on [n] whose injective restrictions to maximal proper subsets of [n] are even and let Δ_n denote the submonoid of Σ_n generated by transformations of rank at least n−1. In this paper, we present descriptions of Γ_n, Δ_n and Σ_n, determine their cardinalities and ranks, and provide minimal generating sets for each of them.&lt;/p&gt;
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