Abstract: Given a rewriting system, we'd like to be able to identify algebraic properties of the group by looking for conditions to check in the rewriting system. In 1986, Avenhaus, Madlener, and Otto proved sufficient conditions for a rewriting system to generate a plain group (a free product of free and finite groups). Gilman conjectured that those conditions could be weakened, and the question remains open. I'll discuss joint work with Adam Piggott addressing this conjecture. (This talk will be accessible even without background knowledge of rewriting systems.)
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