Finite Bruck loops

Aschbacher, Michael; Kinyon, Michael; Phillips, J.

doi:10.1090/S0002-9947-05-03778-5

Finite Bruck loops
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by Michael Aschbacher, Michael K. Kinyon and J. D. Phillips PDF

Trans. Amer. Math. Soc. 358 (2006), 3061-3075 Request permission

Abstract:

Bruck loops are Bol loops satisfying the automorphic inverse property. We prove a structure theorem for finite Bruck loops $X$, showing that $X$ is essentially the direct product of a Bruck loop of odd order with a $2$-element Bruck loop. The former class of loops is well understood. We identify the minimal obstructions to the conjecture that all finite $2$-element Bruck loops are $2$-loops, leaving open the question of whether such obstructions actually exist.

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