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〈a, b | aa=a, aaa=b〉

Monoid presentation of length 7

Properties

Completion parameters

Complete rewriting system

  1. b ⇒ a
  2. a2 ⇒ a

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1a
11a
aaa

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

1 unique, 1991 total

Length:Presentation:Description:Related:
4 〈a, b | aa=1, ab=1〉 Isomorphic to ℤ2 1990 isomorphic

Other isomorphic instances

46 total

Length:Presentation:
7〈a, b | ab=a, abb=b〉
8〈a, b | aa=a, aaaa=b〉
8〈a, b | ab=a, abbb=b〉
9〈a, b | aab=a, aabb=b〉
9〈a, b | aab=a, abab=b〉
9〈a, b | aab=a, abba=b〉
9〈a, b | aab=a, abbb=b〉
9〈a, b | aba=a, abba=b〉
9〈a, b | aa=a, aaaaa=b〉
9〈a, b | ab=a, abbbb=b〉
10〈a, b | aa=a, aaaaaa=b〉
10〈a, b | ab=a, abbbbb=b〉
11〈a, b | aaab=a, aaabb=b〉
11〈a, b | aaab=a, aabab=b〉
11〈a, b | aaab=a, aabba=b〉
11〈a, b | aaab=a, abaab=b〉
11〈a, b | aaab=a, ababa=b〉
11〈a, b | aaab=a, abbaa=b〉
11〈a, b | aaba=a, aabba=b〉
11〈a, b | aaba=a, ababa=b〉
11〈a, b | aaba=a, abbaa=b〉
11〈a, b | aabb=a, abbbb=b〉
11〈a, b | abab=a, abbbb=b〉
11〈a, b | abba=b, aaaab=a〉
11〈a, b | abba=b, aaaba=a〉
11〈a, b | abba=b, aabaa=a〉
11〈a, b | aab=a, aaabbb=b〉
11〈a, b | aab=a, aababb=b〉
11〈a, b | aab=a, aabbab=b〉
11〈a, b | aab=a, aabbba=b〉
11〈a, b | aab=a, aabbbb=b〉
11〈a, b | aab=a, abaabb=b〉
11〈a, b | aab=a, ababab=b〉
11〈a, b | aab=a, ababba=b〉
11〈a, b | aab=a, ababbb=b〉
11〈a, b | aab=a, abbaab=b〉
11〈a, b | aab=a, abbaba=b〉
11〈a, b | aab=a, abbabb=b〉
11〈a, b | aab=a, abbbaa=b〉
11〈a, b | aab=a, abbbab=b〉
11〈a, b | aab=a, abbbba=b〉
11〈a, b | aba=a, aabbba=b〉
11〈a, b | aba=a, ababba=b〉
11〈a, b | aba=a, abbbba=b〉
11〈a, b | aa=a, aaaaaaa=b〉
11〈a, b | ab=a, abbbbbb=b〉