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〈a, b | aaa=1, babb=a〉

Monoid presentation of length 8

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. b9 ⇒ 1
  2. ba ⇒ ab7
  3. a3 ⇒ 1

Right Cayley graph

Left Cayley graph

Others with same cardinality

14 unique, 72 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
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, aabbab=1〉 Finite non-Abelian group with 27 elements 23 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

21 total

Length:Presentation:
9〈a, b | aaa=1, aababb=1〉
9〈a, b | aaa=1, ababba=1〉
9〈a, b | aaa=1, abbaab=1〉
9〈a, b | aaa=1, baabab=1〉
10〈a, b | aaa=1, ababb=aa〉
11〈a, b | aaaa=a, aababb=1〉
11〈a, b | aaaa=a, ababba=1〉
11〈a, b | aaaa=a, abbaab=1〉
11〈a, b | aaaa=a, baabab=1〉
11〈a, b | aaab=b, aababb=1〉
11〈a, b | aaab=b, ababba=1〉
11〈a, b | aaab=b, abbaab=1〉
11〈a, b | aaab=b, baabab=1〉
11〈a, b | aaab=b, babbaa=1〉
11〈a, b | aaab=b, bbaaba=1〉
11〈a, b | aaa=1, aaababb=a〉
11〈a, b | aaa=1, aababba=a〉
11〈a, b | aaa=1, aabbaab=a〉
11〈a, b | aaa=1, abaabab=a〉
11〈a, b | aaa=1, baaaabb=a〉
11〈a, b | aaa=1, babb=aaaa〉