Finite Bruck Loops
摘要
A loop is said to be a Bruck loop if it satisfies the (right) Bol identity and the automorphic inverse property . If is a finite Bruck loop and is the group generated by all right translations , then we show that and are central products and , where () is the subloop (subgroup) generated by all 2-elements, and () is the largest normal subloop (subgroup) of odd order. In particular, if is solvable, then these central products are direct products. We also give a set of necessary conditions that must hold for a finite Bruck loop to be nonsolvable but have each proper section solvable; in particular, must be simple and consist of 2-elements, while the quotient of by its largest normal 2-subgroup must be isomorphic to , with .
引用
@article{arxiv.math/0401193,
title = {Finite Bruck Loops},
author = {Michael Aschbacher and Michael K. Kinyon and J. D. Phillips},
journal= {arXiv preprint arXiv:math/0401193},
year = {2008}
}
备注
16 pages, AMS-TeX