Back

〈a, b | aaa=1, aabbab=1〉

Monoid presentation of length 9

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. b9 ⇒ 1
  2. ba ⇒ ab4
  3. a3 ⇒ 1

Right Cayley graph

Left Cayley graph

Others with same cardinality

14 unique, 70 total

Length:Presentation:Description:Related:
8 〈a, b | bab=aa, bbb=1〉 Finite non-commutative monoid with 27 elements 7 isomorphic
8 〈a, b | aaa=1, abba=b〉 Finite non-commutative monoid with 27 elements 7 isomorphic
8 〈a, b | aaa=1, babb=a〉 Finite non-Abelian group with 27 elements 21 isomorphic
9 〈a, b | bab=aba, bbb=1〉 Finite non-commutative monoid with 27 elements 3 isomorphic
9 〈a, b | bab=aa, bbb=b〉 Finite non-commutative monoid with 27 elements 1 isomorphic
9 〈a, b | aaa=1, ababa=b〉 Finite non-commutative monoid with 27 elements 3 isomorphic
10 〈a, b | aaa=aa, aba=bb〉 Finite non-commutative monoid with 27 elements
10 〈a, b | aaa=1, abaaba=b〉 Finite non-commutative monoid with 27 elements 1 isomorphic
10 〈a, b | aaa=1, baab=aba〉 Finite non-commutative monoid with 27 elements 1 isomorphic
11 〈a, b | aaba=b, aaabbb=1〉 Finite non-Abelian group with 27 elements 7 isomorphic
11 〈a, b | aaba=b, aabbab=1〉 Finite non-Abelian group with 27 elements 5 isomorphic
11 〈a, b | aaa=bb, aabaa=b〉 Finite non-commutative monoid with 27 elements
11 〈a, b | aaa=a, abbbbb=b〉 Finite non-commutative monoid with 27 elements
11 〈a, b | aba=b, bbbb=aaa〉 Finite non-commutative monoid with 27 elements

Other isomorphic instances

23 total

Length:Presentation:
9〈a, b | aaa=1, abaabb=1〉
10〈a, b | aaa=1, abbab=aa〉
10〈a, b | aaa=1, baabb=aa〉
11〈a, b | aaaa=a, aabbab=1〉
11〈a, b | aaaa=a, abaabb=1〉
11〈a, b | aaab=b, aabbab=1〉
11〈a, b | aaab=b, abaabb=1〉
11〈a, b | aaab=b, abbaba=1〉
11〈a, b | aaab=b, baabba=1〉
11〈a, b | aaab=b, babaab=1〉
11〈a, b | aaab=b, bbabaa=1〉
11〈a, b | aaba=b, aababb=1〉
11〈a, b | aaba=b, ababba=1〉
11〈a, b | aaba=b, abbaab=1〉
11〈a, b | aaba=b, baabab=1〉
11〈a, b | aaba=b, babbaa=1〉
11〈a, b | aaba=b, bbaaba=1〉
11〈a, b | aaa=1, aaabbab=a〉
11〈a, b | aaa=1, aabaabb=a〉
11〈a, b | aaa=1, aabbaba=a〉
11〈a, b | aaa=1, abaabba=a〉
11〈a, b | aaa=1, ababaab=a〉
11〈a, b | aaa=1, baaabab=a〉