### Cross-sections and direct products of monoids:

Algebra and Geometry Seminar

6th December 2018, 4:30 pm – 5:30 pm

Howard House, 4th Floor Seminar Room

A cross-section (or set of normal forms) for a monoid M is a language (over some generating set for M) of unique representatives for elements of M.

A monoid is Markov if it has a prefix-closed regular cross-section over some generating set.

I will give an example of a monoid M that has no regular cross-section, but such that the direct product of M with the integers is Markov. Thus the class of Markov monoids is not closed under taking direct factors.

This is joint work with Alan Cain and Victor Maltcev.

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