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〈a, b | aa=1, abab=bbb〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. b7 ⇒ b4
  2. bab ⇒ ab3
  3. a2 ⇒ 1

Idempotents

3 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

7 unique, 9 total

Length:Presentation:Description:Related:
10 〈a, b | aaa=bb, baab=a〉 Finite non-commutative monoid with 26 elements
10 〈a, b | bb=aa, ababa=a〉 Finite non-commutative monoid with 26 elements
10 〈a, b | bb=aa, ababa=b〉 Finite non-commutative monoid with 26 elements
10 〈a, b | aa=1, ababab=bb〉 Finite non-commutative monoid with 26 elements 1 isomorphic
11 〈a, b | aba=bb, bbabb=a〉 Finite non-commutative monoid with 26 elements
11 〈a, b | aba=b, babbb=aa〉 Finite non-commutative monoid with 26 elements
11 〈a, b | aa=1, abbbbbbb=b〉 Finite non-commutative monoid with 26 elements 1 isomorphic

Other isomorphic instances

10 total

Length:Presentation:
9〈a, b | aa=1, abbb=bab〉
11〈a, b | aa=1, aaabab=bbb〉
11〈a, b | aa=1, aaabbb=bab〉
11〈a, b | aa=1, abaaab=bbb〉
11〈a, b | aa=1, abaabb=bab〉
11〈a, b | aa=1, abbaab=bab〉
11〈a, b | aa=1, aabab=abbb〉
11〈a, b | aa=1, aabbb=abab〉
11〈a, b | aa=1, baaab=abbb〉
11〈a, b | aa=1, baabb=abab〉

Other anti-isomorphic instances

7 total

Length:Presentation:
11〈a, b | aa=1, aababa=bbb〉
11〈a, b | aa=1, aabbba=bab〉
11〈a, b | aa=1, aabab=bbba〉
11〈a, b | aa=1, aabbb=baba〉
11〈a, b | aa=1, ababa=abbb〉
11〈a, b | aa=1, abbba=abab〉
11〈a, b | aa=1, baabb=baba〉