Back

〈a, b | aaa=b, abb=b〉

Monoid presentation of length 8

Properties

Completion parameters

Complete rewriting system

  1. a7 ⇒ a3
  2. b ⇒ a3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aa2a3a4a5a6
11aa2a3a4a5a6
aaa2a3a4a5a6a3
a2a2a3a4a5a6a3a4
a3a3a4a5a6a3a4a5
a4a4a5a6a3a4a5a6
a5a5a6a3a4a5a6a3
a6a6a3a4a5a6a3a4

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

32 unique, 1179 total

Length:Presentation:Description:Related:
7 〈a, b | aaa=b, abb=1〉 Isomorphic to ℤ7 763 isomorphic
8 〈a, b | aaa=b, abb=a〉 Finite commutative monoid with 7 elements 59 isomorphic
8 〈a, b | aa=b, abbb=b〉 Finite commutative monoid with 7 elements 82 isomorphic
8 〈a, b | ab=a, baaa=b〉 Finite non-commutative monoid with 7 elements 34 isomorphic
9 〈a, b | aaa=ab, baa=b〉 Finite non-commutative monoid with 7 elements
9 〈a, b | aaa=bb, aab=b〉 Finite commutative monoid with 7 elements 5 isomorphic
9 〈a, b | aab=aa, bbb=a〉 Finite commutative monoid with 7 elements 35 isomorphic
9 〈a, b | aab=ab, bbb=a〉 Finite commutative monoid with 7 elements 50 isomorphic
9 〈a, b | aab=a, baaa=b〉 Finite non-commutative monoid with 7 elements 10 isomorphic
9 〈a, b | aab=b, babb=a〉 Finite commutative monoid with 7 elements 20 isomorphic
9 〈a, b | aba=a, aaab=b〉 Finite non-commutative monoid with 7 elements 5 isomorphic
9 〈a, b | ab=aa, aaa=bb〉 Finite non-commutative monoid with 7 elements 3 isomorphic
9 〈a, b | bb=aa, aaa=ab〉 Finite non-commutative monoid with 7 elements 1 isomorphic
9 〈a, b | bb=aa, aab=ab〉 Finite non-commutative monoid with 7 elements 1 isomorphic
9 〈a, b | ab=a, bbb=baa〉 Finite non-commutative monoid with 7 elements 5 isomorphic
10 〈a, b | aba=aaa, abb=b〉 Finite non-commutative monoid with 7 elements
10 〈a, b | aba=aaa, baa=b〉 Finite non-commutative monoid with 7 elements
10 〈a, b | abb=aab, bbb=a〉 Finite commutative monoid with 7 elements 42 isomorphic
10 〈a, b | aaab=a, baaa=b〉 Finite non-commutative monoid with 7 elements 8 isomorphic
10 〈a, b | aaab=b, aaba=a〉 Finite non-commutative monoid with 7 elements 1 isomorphic
10 〈a, b | aaa=a, aabba=b〉 Finite non-commutative monoid with 7 elements
10 〈a, b | ab=a, aaaaa=bb〉 Finite commutative monoid with 7 elements 5 isomorphic
10 〈a, b | ab=a, bbbbb=aa〉 Finite commutative monoid with 7 elements 2 isomorphic
10 〈a, b | ab=a, bbbbb=ba〉 Finite non-commutative monoid with 7 elements 1 isomorphic
10 〈a, b | ab=a, aaaa=bbb〉 Finite commutative monoid with 7 elements 4 isomorphic
10 〈a, b | ab=a, bbba=bbb〉 Finite non-commutative monoid with 7 elements 3 isomorphic
10 〈a, b | ab=a, bbbb=aaa〉 Finite commutative monoid with 7 elements 3 isomorphic
10 〈a, b | ab=a, bbbb=bba〉 Finite non-commutative monoid with 7 elements 1 isomorphic
11 〈a, b | aaab=b, aaaba=a〉 Finite non-commutative monoid with 7 elements 3 isomorphic
11 〈a, b | abba=b, aabab=a〉 Finite non-commutative monoid with 7 elements 1 isomorphic
11 〈a, b | aaa=a, aababa=b〉 Finite non-commutative monoid with 7 elements
11 〈a, b | aab=b, aaba=aaa〉 Finite non-commutative monoid with 7 elements

Other isomorphic instances

44 total

Length:Presentation:
8〈a, b | aaa=b, bab=b〉
9〈a, b | aa=b, abbb=ab〉
9〈a, b | aa=b, abbb=ba〉
9〈a, b | aa=b, babb=ab〉
9〈a, b | aa=b, babb=ba〉
10〈a, b | bab=aaa, bba=b〉
10〈a, b | aaa=ab, aabb=b〉
10〈a, b | aaa=ab, abab=b〉
10〈a, b | aaa=ab, abba=b〉
10〈a, b | aaa=b, aaaab=b〉
10〈a, b | aaa=b, aaaba=b〉
10〈a, b | aaa=b, aabaa=b〉
10〈a, b | aaa=b, abb=aaa〉
10〈a, b | aaa=b, bab=aaa〉
10〈a, b | aab=a, bbb=aab〉
10〈a, b | aba=a, bbb=aba〉
10〈a, b | aa=b, aaabb=ab〉
10〈a, b | aa=b, aaabb=ba〉
10〈a, b | aa=b, aabab=ab〉
10〈a, b | aa=b, aabab=ba〉
10〈a, b | aa=b, aabba=ab〉
10〈a, b | aa=b, aabba=ba〉
10〈a, b | aa=b, abaab=ab〉
10〈a, b | aa=b, abaab=ba〉
10〈a, b | aa=b, ababa=ab〉
10〈a, b | aa=b, baaab=ab〉
10〈a, b | aa=b, abbb=aaa〉
10〈a, b | aa=b, babb=aaa〉
11〈a, b | aaa=ab, aaaab=b〉
11〈a, b | aaa=ab, aaaba=b〉
11〈a, b | aaa=ab, aabaa=b〉
11〈a, b | aaa=ab, abaaa=b〉
11〈a, b | aa=b, aaaaab=ab〉
11〈a, b | aa=b, aaaaab=ba〉
11〈a, b | aa=b, aaaaba=ab〉
11〈a, b | aa=b, aaaaba=ba〉
11〈a, b | aa=b, aaabaa=ab〉
11〈a, b | aa=b, aaabaa=ba〉
11〈a, b | aa=b, aaabb=aaa〉
11〈a, b | aa=b, aabab=aaa〉
11〈a, b | aa=b, aabba=aaa〉
11〈a, b | aa=b, abaab=aaa〉
11〈a, b | aa=b, ababa=aaa〉
11〈a, b | aa=b, baaab=aaa〉