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〈a, b | aba=bb, aabbb=1〉

Monoid presentation of length 10

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. b12 ⇒ 1
  2. ba ⇒ ab5
  3. a2 ⇒ b9

Cayley table

1ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8b9ab9b10ab10b11ab11
11ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8b9ab9b10ab10b11ab11
aab9abb10ab2b11ab31ab4bab5b2ab6b3ab7b4ab8b5ab9b6ab10b7ab11b8
bbab5b2ab6b3ab7b4ab8b5ab9b6ab10b7ab11b8ab9abb10ab2b11ab31ab4
ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8b9ab9b10ab10b11ab111ab
b2b2ab10b3ab11b4ab5abb6ab2b7ab3b8ab4b9ab5b10ab6b11ab71ab8bab9
ab2ab2b7ab3b8ab4b9ab5b10ab6b11ab71ab8bab9b2ab10b3ab11b4ab5abb6
b3b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8b9ab9b10ab10b11ab111ababb2ab2
ab3ab31ab4bab5b2ab6b3ab7b4ab8b5ab9b6ab10b7ab11b8ab9abb10ab2b11
b4b4ab8b5ab9b6ab10b7ab11b8ab9abb10ab2b11ab31ab4bab5b2ab6b3ab7
ab4ab4b5ab5b6ab6b7ab7b8ab8b9ab9b10ab10b11ab111ababb2ab2b3ab3b4
b5b5abb6ab2b7ab3b8ab4b9ab5b10ab6b11ab71ab8bab9b2ab10b3ab11b4a
ab5ab5b10ab6b11ab71ab8bab9b2ab10b3ab11b4ab5abb6ab2b7ab3b8ab4b9
b6b6ab6b7ab7b8ab8b9ab9b10ab10b11ab111ababb2ab2b3ab3b4ab4b5ab5
ab6ab6b3ab7b4ab8b5ab9b6ab10b7ab11b8ab9abb10ab2b11ab31ab4bab5b2
b7b7ab11b8ab9abb10ab2b11ab31ab4bab5b2ab6b3ab7b4ab8b5ab9b6ab10
ab7ab7b8ab8b9ab9b10ab10b11ab111ababb2ab2b3ab3b4ab4b5ab5b6ab6b7
b8b8ab4b9ab5b10ab6b11ab71ab8bab9b2ab10b3ab11b4ab5abb6ab2b7ab3
ab8ab8bab9b2ab10b3ab11b4ab5abb6ab2b7ab3b8ab4b9ab5b10ab6b11ab71
b9b9ab9b10ab10b11ab111ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8
ab9ab9b6ab10b7ab11b8ab9abb10ab2b11ab31ab4bab5b2ab6b3ab7b4ab8b5
b10b10ab2b11ab31ab4bab5b2ab6b3ab7b4ab8b5ab9b6ab10b7ab11b8ab9ab
ab10ab10b11ab111ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8b9ab9b10
b11b11ab71ab8bab9b2ab10b3ab11b4ab5abb6ab2b7ab3b8ab4b9ab5b10ab6
ab11ab11b4ab5abb6ab2b7ab3b8ab4b9ab5b10ab6b11ab71ab8bab9b2ab10b3

Right Cayley graph

Left Cayley graph

Others with same cardinality

14 unique, 55 total

Length:Presentation:Description:Related:
8 〈a, b | aab=ba, bbb=1〉 Finite non-commutative monoid with 24 elements 6 isomorphic
9 〈a, b | aaa=1, aaba=bb〉 Finite non-commutative monoid with 24 elements 5 isomorphic
9 〈a, b | aaa=1, abab=ba〉 Finite non-commutative monoid with 24 elements 2 isomorphic, 3 anti-isomorphic
10 〈a, b | bb=aa, aaabab=1〉 Finite non-Abelian group with 24 elements 2 isomorphic
10 〈a, b | aaa=1, abaab=ba〉 Finite non-commutative monoid with 24 elements 1 isomorphic
11 〈a, b | ababa=b, abbaa=1〉 Finite non-Abelian group with 24 elements 2 isomorphic
11 〈a, b | aaaab=1, bbbbbb=1〉 Isomorphic to ℤ24 8 isomorphic
11 〈a, b | aaabb=1, bababa=1〉 Finite non-Abelian group with 24 elements 3 isomorphic
11 〈a, b | abba=b, aaabbb=1〉 Finite non-Abelian group with 24 elements 2 isomorphic
11 〈a, b | abba=b, ababab=1〉 Finite non-Abelian group with 24 elements
11 〈a, b | aba=b, aaabbbb=1〉 Finite non-Abelian group with 24 elements 7 isomorphic
11 〈a, b | aba=a, aaaab=bb〉 Finite non-commutative monoid with 24 elements
11 〈a, b | aba=b, aaaa=bab〉 Finite non-commutative monoid with 24 elements
11 〈a, b | aaa=1, aabaaba=b〉 Finite non-commutative monoid with 24 elements

Other isomorphic instances

22 total

Length:Presentation:
10〈a, b | aba=bb, abbba=1〉
10〈a, b | aba=bb, baabb=1〉
11〈a, b | aabaa=b, aabba=1〉
11〈a, b | aabaa=b, baaab=1〉
11〈a, b | aabaa=b, bbaaa=1〉
11〈a, b | aaabb=1, abbbab=1〉
11〈a, b | aaabb=1, bababb=1〉
11〈a, b | aaabb=1, babbba=1〉
11〈a, b | aaabb=1, bbabab=1〉
11〈a, b | aaabb=1, bbbaba=1〉
11〈a, b | aabba=1, ababbb=1〉
11〈a, b | aabba=1, abbbab=1〉
11〈a, b | aabba=1, bababb=1〉
11〈a, b | aabba=1, babbba=1〉
11〈a, b | aabba=1, bbabab=1〉
11〈a, b | aabba=1, bbbaba=1〉
11〈a, b | abbba=1, aaabab=1〉
11〈a, b | abbba=1, aababa=1〉
11〈a, b | abbba=1, abaaab=1〉
11〈a, b | aba=bb, aaabab=1〉
11〈a, b | aba=bb, aababa=1〉
11〈a, b | aba=bb, abaaab=1〉