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〈a, b | aa=1, ababbb=b〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. a2 ⇒ 1
  2. bab ⇒ ab2
  3. b4 ⇒ b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1ababbab2abaab2b2ab3ab2aab3b3aab3a
11ababbab2abaab2b2ab3ab2aab3b3aab3a
aa1abbabaab2bab2ab2aab3b2ab3ab3ab3a
bbbab2ab2b2ab3ab2aab3b3abab3aabbaaba
abababaab2b2ab2aab3b2ab3ab3aabb3abababa
bababab2b2ab2aab3b2ab3ab3aabb3abababa
b2b2b2ab3ab3b3abab3aabbab2abaab2b2aab2a
abaabaabb2ab2b2ab3ab2aab3b3abab3aabbaaba
ab2ab2ab2aab3b3ab3aabb3ababaab2bab2ab2ab2a
b2ab2ab2ab3b3ab3aabb3ababaab2bab2ab2ab2a
b3b3b3ababbab2abaab2b2ab3ab2aab3b3aab3a
ab2aab2aab2b3ab3b3abab3aabbab2abaab2b2aab2a
ab3ab3ab3aabbabaab2bab2ab2aab3b2ab3ab3ab3a
b3ab3ab3abbabaab2bab2ab2aab3b2ab3ab3ab3a
ab3aab3aab3babbab2abaab2b2ab3ab2aab3b3aab3a

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

35 unique, 279 total

Length:Presentation:Description:Related:
8 〈a, b | aa=1, abbbb=b〉 Finite non-commutative monoid with 14 elements 14 isomorphic, 7 anti-isomorphic
9 〈a, b | aba=bb, bab=a〉 Finite non-commutative monoid with 14 elements 1 isomorphic
9 〈a, b | aa=a, bbbb=ab〉 Finite non-commutative monoid with 14 elements 2 isomorphic
10 〈a, b | aaaa=bb, abbb=1〉 Isomorphic to ℤ14 165 isomorphic
10 〈a, b | aab=bb, bbba=a〉 Finite non-commutative monoid with 14 elements 5 isomorphic
10 〈a, b | aab=bb, aba=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
10 〈a, b | aab=b, bbba=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaaa=ab, baab=b〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | aaaa=bb, abbb=a〉 Finite commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aaaa=bb, abbb=b〉 Finite commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aabb=aa, baab=b〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | abab=aa, abba=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | abab=aa, baaa=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaaa=b, aabbb=a〉 Finite commutative monoid with 14 elements 15 isomorphic
11 〈a, b | aaaa=b, aabbb=b〉 Finite commutative monoid with 14 elements 5 isomorphic
11 〈a, b | aaa=bb, abbbb=b〉 Finite commutative monoid with 14 elements 11 isomorphic
11 〈a, b | aaa=bb, babbb=a〉 Finite commutative monoid with 14 elements
11 〈a, b | aab=aa, baaaa=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaa=ab, baab=bb〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aaa=bb, bbbb=ab〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aab=bb, abab=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aba=bb, bbbb=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aab=b, abbaa=aa〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | aab=b, babba=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aab=a, bbbb=baa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | ab=aa, bbbbb=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbbb=ba〉 Finite non-commutative monoid with 14 elements
11 〈a, b | ab=aa, bbaa=bbb〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbb=aaa〉 Finite non-commutative monoid with 14 elements 3 isomorphic
11 〈a, b | ab=aa, bbbb=baa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbb=bba〉 Finite non-commutative monoid with 14 elements
11 〈a, b | bb=aa, abab=aaa〉 Finite non-commutative monoid with 14 elements 2 anti-isomorphic
11 〈a, b | aa=a, bbbbbbb=a〉 Finite commutative monoid with 14 elements
11 〈a, b | aa=b, bbbbbbb=b〉 Finite commutative monoid with 14 elements
11 〈a, b | ab=a, bbaaaa=bb〉 Finite non-commutative monoid with 14 elements

Other isomorphic instances

27 total

Length:Presentation:
9〈a, b | aa=1, abbabb=b〉
9〈a, b | aa=1, babbb=ab〉
9〈a, b | aa=1, bbabb=ab〉
11〈a, b | aa=1, aaababbb=b〉
11〈a, b | aa=1, aaabbabb=b〉
11〈a, b | aa=1, abaaabbb=b〉
11〈a, b | aa=1, abaababb=b〉
11〈a, b | aa=1, ababaabb=b〉
11〈a, b | aa=1, abababab=b〉
11〈a, b | aa=1, ababbaab=b〉
11〈a, b | aa=1, abbaaabb=b〉
11〈a, b | aa=1, abbabaab=b〉
11〈a, b | aa=1, aababbb=ab〉
11〈a, b | aa=1, aabbabb=ab〉
11〈a, b | aa=1, ababbba=ba〉
11〈a, b | aa=1, baaabbb=ab〉
11〈a, b | aa=1, baababb=ab〉
11〈a, b | aa=1, babaabb=ab〉
11〈a, b | aa=1, bababab=ab〉
11〈a, b | aa=1, bbaaabb=ab〉
11〈a, b | aa=1, ababbb=aab〉
11〈a, b | aa=1, ababbb=baa〉
11〈a, b | aa=1, abbabb=aab〉
11〈a, b | aa=1, abbabb=baa〉
11〈a, b | aa=1, babbb=aaab〉
11〈a, b | aa=1, babbb=abaa〉
11〈a, b | aa=1, bbabb=aaab〉

Other anti-isomorphic instances

10 total

Length:Presentation:
11〈a, b | aa=1, aabbabba=b〉
11〈a, b | aa=1, aabbbaba=b〉
11〈a, b | aa=1, aabbabb=ba〉
11〈a, b | aa=1, aabbbab=ba〉
11〈a, b | aa=1, abbabba=ab〉
11〈a, b | aa=1, baababb=ba〉
11〈a, b | aa=1, baabbab=ba〉
11〈a, b | aa=1, abbabb=aba〉
11〈a, b | aa=1, abbbab=aba〉
11〈a, b | aa=1, bbabb=aaba〉