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〈a, b | aab=aa, bbb=a〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. b7 ⇒ b6
  2. a ⇒ b3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1bb2b3b4b5b6
11bb2b3b4b5b6
bbb2b3b4b5b6b6
b2b2b3b4b5b6b6b6
b3b3b4b5b6b6b6b6
b4b4b5b6b6b6b6b6
b5b5b6b6b6b6b6b6
b6b6b6b6b6b6b6b6

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

32 unique, 1188 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 | aaa=b, abb=b〉 Finite commutative monoid with 7 elements 44 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=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

35 total

Length:Presentation:
9〈a, b | aba=aa, bbb=a〉
10〈a, b | ab=a, bbbbbb=a〉
10〈a, b | aa=b, abbb=bbb〉
10〈a, b | aa=b, babb=bbb〉
11〈a, b | aab=ab, aaaaa=b〉
11〈a, b | aab=ba, aaaaa=b〉
11〈a, b | aba=ab, aaaaa=b〉
11〈a, b | aaa=b, aaaab=bb〉
11〈a, b | aaa=b, aaaba=bb〉
11〈a, b | aaa=b, aabaa=bb〉
11〈a, b | aaa=b, aaab=abb〉
11〈a, b | aaa=b, aaab=bab〉
11〈a, b | aaa=b, aaab=bba〉
11〈a, b | aaa=b, aaba=abb〉
11〈a, b | aaa=b, aaba=bab〉
11〈a, b | aaa=b, aaba=bba〉
11〈a, b | ab=a, bbbbbb=ab〉
11〈a, b | aa=b, aaabb=bbb〉
11〈a, b | aa=b, aabab=bbb〉
11〈a, b | aa=b, aabba=bbb〉
11〈a, b | aa=b, abaab=bbb〉
11〈a, b | aa=b, ababa=bbb〉
11〈a, b | aa=b, baaab=bbb〉
11〈a, b | aa=b, abbb=aabb〉
11〈a, b | aa=b, abbb=abab〉
11〈a, b | aa=b, abbb=abba〉
11〈a, b | aa=b, baab=abbb〉
11〈a, b | aa=b, baba=abbb〉
11〈a, b | aa=b, babb=aabb〉
11〈a, b | aa=b, babb=abab〉
11〈a, b | aa=b, babb=abba〉
11〈a, b | aa=b, babb=baab〉
11〈a, b | aa=b, babb=baba〉
11〈a, b | aa=b, bbaa=abbb〉
11〈a, b | aa=b, bbaa=babb〉