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〈a, b | aa=1, ababbbb=1〉

Monoid presentation of length 9

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. b15 ⇒ 1
  2. ba ⇒ ab11
  3. a2 ⇒ 1

Right Cayley graph

Left Cayley graph

Others with same cardinality

18 unique, 70 total

Length:Presentation:Description:Related:
9 〈a, b | aaa=bb, abab=1〉 Finite non-Abelian group with 30 elements 8 isomorphic
9 〈a, b | aab=a, bbbbb=1〉 Finite non-commutative monoid with 30 elements 2 isomorphic, 1 anti-isomorphic
9 〈a, b | ab=aa, bbbbb=1〉 Finite non-commutative monoid with 30 elements 2 isomorphic
9 〈a, b | aaa=1, abbbb=b〉 Finite non-commutative monoid with 30 elements 6 isomorphic, 3 anti-isomorphic
9 〈a, b | aaa=1, bbbb=ab〉 Finite non-commutative monoid with 30 elements 7 isomorphic, 2 anti-isomorphic
10 〈a, b | aabb=a, bbbbb=1〉 Finite non-commutative monoid with 30 elements 1 isomorphic, 1 anti-isomorphic
10 〈a, b | aab=bb, aaaaa=1〉 Finite non-commutative monoid with 30 elements 3 anti-isomorphic
10 〈a, b | aba=ab, bbbbb=1〉 Finite non-commutative monoid with 30 elements
10 〈a, b | aaa=a, bbbb=ab〉 Finite non-commutative monoid with 30 elements
10 〈a, b | ab=aa, bbbbb=b〉 Finite non-commutative monoid with 30 elements
10 〈a, b | aa=1, abababbb=1〉 Finite non-Abelian group with 30 elements 5 isomorphic
11 〈a, b | abba=bbb, baba=1〉 Finite non-Abelian group with 30 elements 8 isomorphic
11 〈a, b | abb=aab, aaaaa=1〉 Finite non-commutative monoid with 30 elements
11 〈a, b | bab=aaa, aabbb=1〉 Finite non-Abelian group with 30 elements 2 isomorphic
11 〈a, b | bbb=aaa, aaba=b〉 Finite non-commutative monoid with 30 elements
11 〈a, b | aba=bb, abbabb=1〉 Finite non-Abelian group with 30 elements 1 isomorphic
11 〈a, b | aaa=aa, bbbb=ab〉 Finite non-commutative monoid with 30 elements
11 〈a, b | ab=aa, bbbbb=bb〉 Finite non-commutative monoid with 30 elements

Other isomorphic instances

53 total

Length:Presentation:
9〈a, b | aa=1, abbbbab=1〉
9〈a, b | aa=1, bababbb=1〉
9〈a, b | aa=1, bbababb=1〉
9〈a, b | aa=1, babbbb=a〉
11〈a, b | aaa=a, ababbbb=1〉
11〈a, b | aaa=a, abbbbab=1〉
11〈a, b | aaa=a, bababbb=1〉
11〈a, b | aaa=a, bbababb=1〉
11〈a, b | aab=b, ababbbb=1〉
11〈a, b | aab=b, abbbbab=1〉
11〈a, b | aab=b, bababbb=1〉
11〈a, b | aab=b, babbbba=1〉
11〈a, b | aab=b, bbababb=1〉
11〈a, b | aab=b, bbbabab=1〉
11〈a, b | aab=b, bbbbaba=1〉
11〈a, b | aa=1, aaababbbb=1〉
11〈a, b | aa=1, aaabbbbab=1〉
11〈a, b | aa=1, aabababbb=1〉
11〈a, b | aa=1, aababbbba=1〉
11〈a, b | aa=1, aabbababb=1〉
11〈a, b | aa=1, aabbbabab=1〉
11〈a, b | aa=1, aabbbbaba=1〉
11〈a, b | aa=1, abaaabbbb=1〉
11〈a, b | aa=1, abaabbbab=1〉
11〈a, b | aa=1, ababaabbb=1〉
11〈a, b | aa=1, abababbba=1〉
11〈a, b | aa=1, ababbaabb=1〉
11〈a, b | aa=1, ababbbaab=1〉
11〈a, b | aa=1, abbaabbab=1〉
11〈a, b | aa=1, abbababba=1〉
11〈a, b | aa=1, abbbaabab=1〉
11〈a, b | aa=1, abbbbaaab=1〉
11〈a, b | aa=1, baaababbb=1〉
11〈a, b | aa=1, baabababb=1〉
11〈a, b | aa=1, baabbabab=1〉
11〈a, b | aa=1, babaaabbb=1〉
11〈a, b | aa=1, bababaabb=1〉
11〈a, b | aa=1, bbaaababb=1〉
11〈a, b | aa=1, aababbbb=a〉
11〈a, b | aa=1, aabbbbab=a〉
11〈a, b | aa=1, abababbb=a〉
11〈a, b | aa=1, ababbbba=a〉
11〈a, b | aa=1, abbababb=a〉
11〈a, b | aa=1, abbbabab=a〉
11〈a, b | aa=1, baaabbbb=a〉
11〈a, b | aa=1, baabbbab=a〉
11〈a, b | aa=1, babaabbb=a〉
11〈a, b | aa=1, babbaabb=a〉
11〈a, b | aa=1, ababbbb=aa〉
11〈a, b | aa=1, abbbbab=aa〉
11〈a, b | aa=1, bababbb=aa〉
11〈a, b | aa=1, bbababb=aa〉
11〈a, b | aa=1, babbbb=aaa〉