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〈a, b | aaa=1, abbbb=b〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. b10 ⇒ b
  2. ab ⇒ b7
  3. a3 ⇒ 1

Idempotents

4 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

18 unique, 114 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, bbbb=ab〉 Finite non-commutative monoid with 30 elements 7 isomorphic, 2 anti-isomorphic
9 〈a, b | aa=1, ababbbb=1〉 Finite non-Abelian group with 30 elements 53 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

6 total

Length:Presentation:
10〈a, b | aaa=1, bbbb=aab〉
11〈a, b | aaa=1, aabbbb=ab〉
11〈a, b | aaa=1, baabbb=ab〉
11〈a, b | aaa=1, bababb=ab〉
11〈a, b | aaa=1, babbab=ab〉
11〈a, b | aaa=1, bbaabb=ab〉

Other anti-isomorphic instances

3 total

Length:Presentation:
11〈a, b | aaa=1, abbbba=ab〉
11〈a, b | aaa=1, baabbb=ba〉
11〈a, b | aaa=1, bababb=ba〉