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International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures
May 21-24, 2002
Vanderbilt University
Nashville, TN, USA

Organizers
Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis, Matthew Valeriote

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Left symmetric left distributive groupoids
by
David Stanovský
Charles University, Prague
Coauthors: E. Jerábek, T. Kepka

Given a group G, the derived operation x*y=xy-1x is left symmetric (i.e. x*(x*y)=y), left distributive (i.e. x*(y*z)=(x*y)*(x*z)) and idempotent. Groupoids satfisfying these identities (shortly LSLDI-groupoids) were widely studied and applied in geometry (see Nobusawa, Pierce, Joyce, etc). We contribute with a description of the equational theory of several LSLDI-operations on a group.

On the other hand, almost nothing was known about generally non-idepotent LSLD-groupoids. We follow the investigations started by T. Kepka. Several non-idempotent LSLD-operations on a group are found and their equational theories are discussed. A structure of subdirectly irreducible non-idempotent LSLD-groupoids is described.

Date received: February 20, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caig-80.