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〈a, b | aa=b, ab=a〉

Monoid presentation of length 6

Properties

Completion parameters

Complete rewriting system

  1. a3 ⇒ a
  2. b ⇒ a2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aa2
11aa2
aaa2a
a2a2aa2

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

5 unique, 2146 total

Length:Presentation:Description:Related:
5 〈a, b | aa=b, ab=1〉 Isomorphic to ℤ3 2029 isomorphic
6 〈a, b | aa=b, ab=b〉 Finite commutative monoid with 3 elements 23 isomorphic
6 〈a, b | ab=a, ba=b〉 Finite non-commutative monoid with 3 elements 61 isomorphic
8 〈a, b | aa=a, abba=b〉 Finite commutative monoid with 3 elements 12 isomorphic
9 〈a, b | aba=a, aabb=b〉 Finite non-commutative monoid with 3 elements 16 isomorphic

Other isomorphic instances

61 total

Length:Presentation:
7〈a, b | aa=b, aaa=a〉
7〈a, b | ab=a, aab=b〉
7〈a, b | ab=a, aba=b〉
8〈a, b | aab=a, aba=b〉
8〈a, b | ab=a, aabb=b〉
8〈a, b | ab=a, abab=b〉
8〈a, b | ab=a, abba=b〉
9〈a, b | aaa=a, aaaa=b〉
9〈a, b | aab=b, aaab=a〉
9〈a, b | aba=b, aaab=a〉
9〈a, b | aba=b, aaba=a〉
9〈a, b | ab=a, aabbb=b〉
9〈a, b | ab=a, ababb=b〉
9〈a, b | ab=a, abbab=b〉
9〈a, b | ab=a, abbba=b〉
10〈a, b | aaa=a, aaaaa=b〉
10〈a, b | aab=a, aaabb=b〉
10〈a, b | aab=a, aabab=b〉
10〈a, b | aab=a, aabba=b〉
10〈a, b | aab=a, abaab=b〉
10〈a, b | aab=a, ababa=b〉
10〈a, b | aab=a, abbaa=b〉
10〈a, b | aab=a, abbbb=b〉
10〈a, b | aab=b, aaaab=a〉
10〈a, b | aba=a, aabba=b〉
10〈a, b | aba=a, ababa=b〉
10〈a, b | aba=b, aaaab=a〉
10〈a, b | aba=b, aaaba=a〉
10〈a, b | aba=b, aabaa=a〉
10〈a, b | ab=a, aabbbb=b〉
10〈a, b | ab=a, ababbb=b〉
10〈a, b | ab=a, abbabb=b〉
10〈a, b | ab=a, abbbab=b〉
10〈a, b | ab=a, abbbba=b〉
11〈a, b | aaab=a, aabbb=b〉
11〈a, b | aaab=a, ababb=b〉
11〈a, b | aaab=a, abbab=b〉
11〈a, b | aaab=a, abbba=b〉
11〈a, b | aaba=a, abbba=b〉
11〈a, b | aabb=a, aabbb=b〉
11〈a, b | aabb=a, abbab=b〉
11〈a, b | aabb=a, abbba=b〉
11〈a, b | abab=a, aabbb=b〉
11〈a, b | abab=a, ababb=b〉
11〈a, b | abab=a, abbab=b〉
11〈a, b | abab=a, abbba=b〉
11〈a, b | abba=a, abbba=b〉
11〈a, b | abba=b, aaabb=a〉
11〈a, b | abba=b, aabba=a〉
11〈a, b | abba=b, abaab=a〉
11〈a, b | aaa=a, aaaaaa=b〉
11〈a, b | aab=b, aaaaab=a〉
11〈a, b | aba=b, aaaaab=a〉
11〈a, b | aba=b, aaaaba=a〉
11〈a, b | aba=b, aaabaa=a〉
11〈a, b | ab=a, aabbbbb=b〉
11〈a, b | ab=a, ababbbb=b〉
11〈a, b | ab=a, abbabbb=b〉
11〈a, b | ab=a, abbbabb=b〉
11〈a, b | ab=a, abbbbab=b〉
11〈a, b | ab=a, abbbbba=b〉