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〈a, b | aaa=1, ababbb=1〉

Monoid presentation of length 9

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. b12 ⇒ 1
  2. b2a ⇒ ab2
  3. a2 ⇒ bab3
  4. aba ⇒ b9

Right Cayley graph

Left Cayley graph

Others with same cardinality

8 unique, 24 total

Length:Presentation:Description:Related:
9 〈a, b | aaab=a, bbbb=1〉 Finite non-commutative monoid with 36 elements 3 isomorphic, 3 anti-isomorphic
9 〈a, b | aaa=ab, bbbb=1〉 Finite non-commutative monoid with 36 elements 1 isomorphic, 5 anti-isomorphic
10 〈a, b | aaa=ab, bbbb=b〉 Finite non-commutative monoid with 36 elements
10 〈a, b | bb=aa, ababab=1〉 Finite non-Abelian group with 36 elements
10 〈a, b | aaa=1, baabbb=a〉 Finite non-Abelian group with 36 elements 4 isomorphic
11 〈a, b | abb=aaa, bbbb=b〉 Finite non-commutative monoid with 36 elements
11 〈a, b | aaa=ab, bbbb=bb〉 Finite non-commutative monoid with 36 elements
11 〈a, b | aab=a, bbbbbb=b〉 Finite non-commutative monoid with 36 elements

Other isomorphic instances

17 total

Length:Presentation:
9〈a, b | aaa=1, abbbab=1〉
9〈a, b | aaa=1, bababb=1〉
10〈a, b | aaa=1, babbb=aa〉
11〈a, b | aaaa=a, ababbb=1〉
11〈a, b | aaaa=a, abbbab=1〉
11〈a, b | aaaa=a, bababb=1〉
11〈a, b | aaab=b, ababbb=1〉
11〈a, b | aaab=b, abbbab=1〉
11〈a, b | aaab=b, bababb=1〉
11〈a, b | aaab=b, babbba=1〉
11〈a, b | aaab=b, bbabab=1〉
11〈a, b | aaab=b, bbbaba=1〉
11〈a, b | aaa=1, aababbb=a〉
11〈a, b | aaa=1, aabbbab=a〉
11〈a, b | aaa=1, abababb=a〉
11〈a, b | aaa=1, ababbba=a〉
11〈a, b | aaa=1, abbabab=a〉