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〈a, b | abba=b, baba=1〉

Monoid presentation of length 9

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. b3 ⇒ 1
  2. ba ⇒ ab2
  3. a2 ⇒ 1

Cayley table

1ababb2ab2
11ababb2ab2
aa1abbab2b2
bbab2b2a1ab
ababb2ab21ab
b2b2ab1ab2ba
ab2ab2bab2ab1

Right Cayley graph

Left Cayley graph

Others with same cardinality

25 unique, 1859 total

Length:Presentation:Description:Related:
6 〈a, b | ab=aa, bb=1〉 Finite non-commutative monoid with 6 elements 22 isomorphic
6 〈a, b | aaa=1, abb=1〉 Isomorphic to ℤ6 1373 isomorphic
6 〈a, b | aa=1, abb=b〉 Finite non-commutative monoid with 6 elements 30 isomorphic
7 〈a, b | ab=aa, bb=b〉 Finite non-commutative monoid with 6 elements
7 〈a, b | aa=a, bbb=a〉 Finite commutative monoid with 6 elements 49 isomorphic
7 〈a, b | aa=b, bbb=a〉 Finite commutative monoid with 6 elements 61 isomorphic
7 〈a, b | aa=b, bbb=b〉 Finite commutative monoid with 6 elements 55 isomorphic
7 〈a, b | aa=1, abab=b〉 Finite non-commutative monoid with 6 elements 31 isomorphic, 22 anti-isomorphic
8 〈a, b | ab=aa, baa=b〉 Finite non-commutative monoid with 6 elements 4 isomorphic
8 〈a, b | ab=aa, bbb=a〉 Finite commutative monoid with 6 elements 46 isomorphic
8 〈a, b | aa=a, abbb=b〉 Finite non-commutative monoid with 6 elements 19 isomorphic
8 〈a, b | aa=a, aab=bb〉 Finite non-commutative monoid with 6 elements 3 isomorphic
8 〈a, b | ab=a, baa=bb〉 Finite non-commutative monoid with 6 elements 12 isomorphic, 1 anti-isomorphic
9 〈a, b | aaa=aa, abb=b〉 Finite non-commutative monoid with 6 elements 5 isomorphic
9 〈a, b | aab=bb, abb=a〉 Finite commutative monoid with 6 elements 13 isomorphic
9 〈a, b | aba=aa, baa=b〉 Finite non-commutative monoid with 6 elements
9 〈a, b | abb=aa, bbb=a〉 Finite commutative monoid with 6 elements 49 isomorphic
9 〈a, b | ab=a, aaaa=bb〉 Finite commutative monoid with 6 elements 14 isomorphic
9 〈a, b | ab=a, bbbb=aa〉 Finite commutative monoid with 6 elements 5 isomorphic
9 〈a, b | ab=a, bbbb=ba〉 Finite non-commutative monoid with 6 elements 2 isomorphic
9 〈a, b | ab=a, bbb=aaa〉 Finite commutative monoid with 6 elements 9 isomorphic
9 〈a, b | ab=a, bbb=bba〉 Finite non-commutative monoid with 6 elements 3 isomorphic
10 〈a, b | aba=aa, aabb=b〉 Finite non-commutative monoid with 6 elements 5 isomorphic
10 〈a, b | aab=b, aaba=aa〉 Finite non-commutative monoid with 6 elements 1 isomorphic
11 〈a, b | aa=a, abbbbba=b〉 Finite commutative monoid with 6 elements

Other isomorphic instances

66 total

Length:Presentation:
9〈a, b | aab=ba, abab=1〉
9〈a, b | aab=ba, baba=1〉
9〈a, b | abab=1, aabba=1〉
9〈a, b | abab=1, abbaa=1〉
9〈a, b | abab=1, abbba=1〉
9〈a, b | abab=1, bbaaa=1〉
10〈a, b | aab=ba, aaabb=1〉
10〈a, b | aab=ba, aabba=1〉
10〈a, b | aab=ba, abbaa=1〉
10〈a, b | aab=ba, baaab=1〉
10〈a, b | aab=ba, bbaaa=1〉
11〈a, b | aaab=aba, abab=1〉
11〈a, b | aaab=aba, baba=1〉
11〈a, b | aaba=baa, abab=1〉
11〈a, b | aaba=baa, baba=1〉
11〈a, b | aabb=aba, baba=1〉
11〈a, b | abba=aab, baba=1〉
11〈a, b | abba=baa, baba=1〉
11〈a, b | abba=bab, baba=1〉
11〈a, b | aabab=a, aabba=1〉
11〈a, b | aabab=a, abbaa=1〉
11〈a, b | aabab=a, abbba=1〉
11〈a, b | aabab=a, baaab=1〉
11〈a, b | aabab=a, baabb=1〉
11〈a, b | aabab=a, bbaaa=1〉
11〈a, b | aabab=a, bbaab=1〉
11〈a, b | aabab=a, bbbaa=1〉
11〈a, b | ababa=a, abbaa=1〉
11〈a, b | ababa=a, abbba=1〉
11〈a, b | ababa=a, baaab=1〉
11〈a, b | ababa=a, baabb=1〉
11〈a, b | abbba=b, baaab=1〉
11〈a, b | abbba=b, bbaaa=1〉
11〈a, b | baaab=a, baabb=1〉
11〈a, b | aaabb=1, abaaba=1〉
11〈a, b | aaabb=1, baabaa=1〉
11〈a, b | aabba=1, aabaab=1〉
11〈a, b | aabba=1, abaaba=1〉
11〈a, b | aabba=1, baabaa=1〉
11〈a, b | abbba=1, abbabb=1〉
11〈a, b | abbba=1, babbab=1〉
11〈a, b | aab=ba, aabaab=1〉
11〈a, b | aab=ba, abaaba=1〉
11〈a, b | aab=ba, baabaa=1〉
11〈a, b | abab=1, aabbaab=1〉
11〈a, b | abab=1, abaabba=1〉
11〈a, b | abab=1, abbaaba=1〉
11〈a, b | abab=1, abbabba=1〉
11〈a, b | abab=1, baabbaa=1〉
11〈a, b | abab=1, bbaabaa=1〉
11〈a, b | abab=1, aabbaa=a〉
11〈a, b | abab=1, abaaab=a〉
11〈a, b | abab=1, abbaaa=a〉
11〈a, b | abab=1, abbaab=a〉
11〈a, b | abab=1, abbbaa=a〉
11〈a, b | abab=1, baaaba=a〉
11〈a, b | abab=1, baabba=a〉
11〈a, b | abab=1, babbaa=b〉
11〈a, b | abab=1, bbaaaa=a〉
11〈a, b | abab=1, bbbaaa=a〉
11〈a, b | abab=1, aabba=ab〉
11〈a, b | abab=1, abaab=aa〉
11〈a, b | abab=1, abaab=ba〉
11〈a, b | abab=1, abbaa=ba〉
11〈a, b | abab=1, baaba=aa〉
11〈a, b | abab=1, baaba=ab〉