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Brookes, Matthew D. G. K.

Congruences on the partial automorphism monoid of a free group action. (English) Zbl 1485.20139

Int. J. Algebra Comput. 31, No. 6, 1147-1176 (2021).
Here, congruences of the the partial automorphism monoid of a finite rank free group action are studied and their description using a Rees congruence are obtained, an idempotent separating congruence and a congruence on a principal factor. This allows to derive upper and lower bounds for the number of congruences.
Reviewer: Jaak Henno (Tallinn)

Cited in 3 Documents

MSC:

20M20 Semigroups of transformations, relations, partitions, etc.
08A30 Subalgebras, congruence relations
16W22 Actions of groups and semigroups; invariant theory (associative rings and algebras)
20M18 Inverse semigroups
20M10 General structure theory for semigroups

Keywords:

free group action; partial automorphism monoid; congruences; subgroups of direct products
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References:

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