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〈a, b | aab=a, bbbb=1〉

Monoid presentation of length 8

Properties

Completion parameters

Complete rewriting system

  1. a5 ⇒ a
  2. ab ⇒ a4
  3. b4 ⇒ 1

Idempotents

5 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2ab3a4ba3b2a2b3aba4b2a3b3a2b2a4b3a3b3a4
11aba2bab2a3ba2b2ab3a4ba3b2a2b3aba4b2a3b3a2b2a4b3a3b3a4
aaa2a4a3aa3a4a2a4a2aa3aa3a4a2a4a3aa2
bbbab2ba2b2ab3ba3b2a2b3a1ba4b2a3b3a2ab2a4b3a3a2b3a4a3a4
a2a2a3aa4a2a4aa3aa3a2a4a2a4aa3aa4a2a3
bababa2ba4ba3baba3ba4ba2ba4ba2baba3baba3ba4ba2ba4ba3baba2
b2b2b2ab3b2a2b3a1b2a3b3a2abb2a4b3a3a2bab3a4a3ba2a4ba3ba4
a3a3a4a2aa3aa2a4a2a4a3aa3aa2a4a2aa3a4
ba2ba2ba3baba4ba2ba4baba3baba3ba2ba4ba2ba4baba3baba4ba2ba3
b2ab2ab2a2b2a4b2a3b2ab2a3b2a4b2a2b2a4b2a2b2ab2a3b2ab2a3b2a4b2a2b2a4b2a3b2ab2a2
b3b3b3a1b3a2abb3a3a2bab2b3a4a3ba2b2aa4ba3b2a2ba4b2a3b2a4
a4a4aa3a2a4a2a3aa3aa4a2a4a2a3aa3a2a4a
ba3ba3ba4ba2baba3baba2ba4ba2ba4ba3baba3baba2ba4ba2baba3ba4
b2a2b2a2b2a3b2ab2a4b2a2b2a4b2ab2a3b2ab2a3b2a2b2a4b2a2b2a4b2ab2a3b2ab2a4b2a2b2a3
b3ab3ab3a2b3a4b3a3b3ab3a3b3a4b3a2b3a4b3a2b3ab3a3b3ab3a3b3a4b3a2b3a4b3a3b3ab3a2
ba4ba4baba3ba2ba4ba2ba3baba3baba4ba2ba4ba2ba3baba3ba2ba4ba
b2a3b2a3b2a4b2a2b2ab2a3b2ab2a2b2a4b2a2b2a4b2a3b2ab2a3b2ab2a2b2a4b2a2b2ab2a3b2a4
b3a2b3a2b3a3b3ab3a4b3a2b3a4b3ab3a3b3ab3a3b3a2b3a4b3a2b3a4b3ab3a3b3ab3a4b3a2b3a3
b2a4b2a4b2ab2a3b2a2b2a4b2a2b2a3b2ab2a3b2ab2a4b2a2b2a4b2a2b2a3b2ab2a3b2a2b2a4b2a
b3a3b3a3b3a4b3a2b3ab3a3b3ab3a2b3a4b3a2b3a4b3a3b3ab3a3b3ab3a2b3a4b3a2b3ab3a3b3a4
b3a4b3a4b3ab3a3b3a2b3a4b3a2b3a3b3ab3a3b3ab3a4b3a2b3a4b3a2b3a3b3ab3a3b3a2b3a4b3a

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

28 unique, 61 total

Length:Presentation:Description:Related:
8 〈a, b | ab=aa, bbbb=1〉 Finite non-commutative monoid with 20 elements 1 isomorphic
9 〈a, b | abab=a, bbbb=1〉 Finite non-commutative monoid with 20 elements 2 isomorphic
9 〈a, b | aba=ab, bbbb=1〉 Finite non-commutative monoid with 20 elements 1 isomorphic, 1 anti-isomorphic
9 〈a, b | ab=aa, bbbb=b〉 Finite non-commutative monoid with 20 elements
10 〈a, b | abb=aab, aaaa=1〉 Finite non-commutative monoid with 20 elements 2 isomorphic
10 〈a, b | baa=abb, abab=1〉 Finite non-Abelian group with 20 elements 1 isomorphic, 1 anti-isomorphic
10 〈a, b | aaaaa=1, abbbb=1〉 Isomorphic to ℤ20 16 isomorphic
10 〈a, b | aab=bb, aaaa=a〉 Finite non-commutative monoid with 20 elements
10 〈a, b | aaa=bb, bab=aa〉 Finite non-commutative monoid with 20 elements 1 isomorphic
10 〈a, b | aba=a, aaaa=bb〉 Finite non-commutative monoid with 20 elements
10 〈a, b | aba=b, aaaa=bb〉 Finite non-commutative monoid with 20 elements
10 〈a, b | ab=aa, bbbb=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaaa=aa, abbb=b〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaab=bb, bbba=a〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaaa=a, bbbbb=a〉 Finite commutative monoid with 20 elements
11 〈a, b | aaaa=b, bbbbb=a〉 Finite commutative monoid with 20 elements
11 〈a, b | aaaa=b, bbbbb=b〉 Finite commutative monoid with 20 elements
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
11 〈a, b | aab=aa, baba=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=aa, aaaa=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=aa, aaab=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=bb, abb=aaa〉 Finite non-commutative monoid with 20 elements
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
11 〈a, b | ab=aa, bbbb=bbb〉 Finite non-commutative monoid with 20 elements

Other isomorphic instances

3 total

Length:Presentation:
10〈a, b | aabb=ab, bbbb=1〉
10〈a, b | abba=ab, bbbb=1〉
10〈a, b | abbb=aa, bbbb=1〉

Other anti-isomorphic instances

1 total

Length:Presentation:
10〈a, b | baab=ab, bbbb=1〉