Jan Mycielski

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A left-distributive algebra (LD) is an algebra satisfying the left-distributive law a · (b · c) = (a · b) · (a · c). A left-distributive idempotent algebra (LDI) additionally satisfies a · a = a. The first part of the thesis concerns LD's, specifically their relationship to the braid groups. For C an LD, a, b ∈ C, let a < L b if and only if b = (((a · c 1)(More)
We prove several cases of the following theorem: Every free group word which is not a proper power can represent every permutation of an infinite set. The remaining cases will be proved in a forthcoming paper of R. C. Lyn-don. Fx denotes a free group freely generated by the set A. The elements of X are called letters, and the elements of Fx are represented(More)