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〈a, b | ab=aa, bbbb=b〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ a2
  2. b4 ⇒ b
  3. a5 ⇒ a2

Idempotents

6 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2ab3a4ba3b2a2b3aba4b2a3b3a2b2a4b3a3b3a4
11aba2bab2a3ba2b2ab3a4ba3b2a2b3aba4b2a3b3a2b2a4b3a3b3a4
aaa2a2a3a3a3a4a4a4a4a2a2a2a2a3a3a3a4a4a2
bbbab2ba2b2ab3ba3b2a2b3abba4b2a3b3a2bab2a4b3a3ba2b3a4ba3ba4
a2a2a3a3a4a4a4a2a2a2a2a3a3a3a3a4a4a4a2a2a3
bababa2ba2ba3ba3ba3ba4ba4ba4ba4ba2ba2ba2ba2ba3ba3ba3ba4ba4ba2
b2b2b2ab3b2a2b3abb2a3b3a2bab2b2a4b3a3ba2b2ab3a4ba3b2a2ba4b2a3b2a4
a3a3a4a4a2a2a2a3a3a3a3a4a4a4a4a2a2a2a3a3a4
ba2ba2ba3ba3ba4ba4ba4ba2ba2ba2ba2ba3ba3ba3ba3ba4ba4ba4ba2ba2ba3
b2ab2ab2a2b2a2b2a3b2a3b2a3b2a4b2a4b2a4b2a4b2a2b2a2b2a2b2a2b2a3b2a3b2a3b2a4b2a4b2a2
b3b3b3abb3a2bab2b3a3ba2b2ab3b3a4ba3b2a2b3aba4b2a3b3a2b2a4b3a3b3a4
a4a4a2a2a3a3a3a4a4a4a4a2a2a2a2a3a3a3a4a4a2
ba3ba3ba4ba4ba2ba2ba2ba3ba3ba3ba3ba4ba4ba4ba4ba2ba2ba2ba3ba3ba4
b2a2b2a2b2a3b2a3b2a4b2a4b2a4b2a2b2a2b2a2b2a2b2a3b2a3b2a3b2a3b2a4b2a4b2a4b2a2b2a2b2a3
b3ab3ab3a2b3a2b3a3b3a3b3a3b3a4b3a4b3a4b3a4b3a2b3a2b3a2b3a2b3a3b3a3b3a3b3a4b3a4b3a2
ba4ba4ba2ba2ba3ba3ba3ba4ba4ba4ba4ba2ba2ba2ba2ba3ba3ba3ba4ba4ba2
b2a3b2a3b2a4b2a4b2a2b2a2b2a2b2a3b2a3b2a3b2a3b2a4b2a4b2a4b2a4b2a2b2a2b2a2b2a3b2a3b2a4
b3a2b3a2b3a3b3a3b3a4b3a4b3a4b3a2b3a2b3a2b3a2b3a3b3a3b3a3b3a3b3a4b3a4b3a4b3a2b3a2b3a3
b2a4b2a4b2a2b2a2b2a3b2a3b2a3b2a4b2a4b2a4b2a4b2a2b2a2b2a2b2a2b2a3b2a3b2a3b2a4b2a4b2a2
b3a3b3a3b3a4b3a4b3a2b3a2b3a2b3a3b3a3b3a3b3a3b3a4b3a4b3a4b3a4b3a2b3a2b3a2b3a3b3a3b3a4
b3a4b3a4b3a2b3a2b3a3b3a3b3a3b3a4b3a4b3a4b3a4b3a2b3a2b3a2b3a2b3a3b3a3b3a3b3a4b3a4b3a2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

28 unique, 65 total

Length:Presentation:Description:Related:
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11 〈a, b | aaaa=aa, abbb=b〉 Finite non-commutative monoid with 20 elements
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11 〈a, b | aaaa=a, bbbbb=a〉 Finite commutative monoid with 20 elements
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11 〈a, b | aab=ba, abbabb=1〉 Finite non-Abelian group with 20 elements 2 isomorphic
11 〈a, b | aba=bb, baaab=a〉 Finite non-commutative monoid with 20 elements
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11 〈a, b | aaaa=1, aaabab=b〉 Finite non-commutative monoid with 20 elements 1 isomorphic
11 〈a, b | aaaa=1, aabab=ab〉 Finite non-commutative monoid with 20 elements 1 isomorphic
11 〈a, b | aba=b, aaaaabb=1〉 Finite non-Abelian group with 20 elements 3 isomorphic
11 〈a, b | aab=a, bbbbb=bb〉 Finite non-commutative monoid with 20 elements
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