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〈a, b | aaa=ab, bbb=a〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. b9 ⇒ b4
  2. a ⇒ b3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1bb2b3b4b5b6b7b8
11bb2b3b4b5b6b7b8
bbb2b3b4b5b6b7b8b4
b2b2b3b4b5b6b7b8b4b5
b3b3b4b5b6b7b8b4b5b6
b4b4b5b6b7b8b4b5b6b7
b5b5b6b7b8b4b5b6b7b8
b6b6b7b8b4b5b6b7b8b4
b7b7b8b4b5b6b7b8b4b5
b8b8b4b5b6b7b8b4b5b6

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

38 unique, 902 total

Length:Presentation:Description:Related:
7 〈a, b | aaa=b, bbb=1〉 Isomorphic to ℤ9 562 isomorphic
8 〈a, b | aaa=a, abb=b〉 Finite non-commutative monoid with 9 elements 2 isomorphic
8 〈a, b | aaa=a, bbb=a〉 Finite commutative monoid with 9 elements 48 isomorphic
8 〈a, b | aaa=b, bbb=a〉 Finite commutative monoid with 9 elements 62 isomorphic
8 〈a, b | aba=b, bab=a〉 Finite non-commutative monoid with 9 elements 3 isomorphic
9 〈a, b | aaa=aa, bbb=a〉 Finite commutative monoid with 9 elements 16 isomorphic
9 〈a, b | aaa=ab, bab=b〉 Finite non-commutative monoid with 9 elements 4 isomorphic
9 〈a, b | aaa=bb, bbb=a〉 Finite commutative monoid with 9 elements 70 isomorphic
9 〈a, b | aaa=a, abab=b〉 Finite non-commutative monoid with 9 elements 2 isomorphic
9 〈a, b | aaa=a, abba=b〉 Finite non-commutative monoid with 9 elements 2 isomorphic
9 〈a, b | aab=b, abba=a〉 Finite non-commutative monoid with 9 elements 13 isomorphic
9 〈a, b | ab=aa, bba=bb〉 Finite non-commutative monoid with 9 elements
9 〈a, b | ab=a, baaaa=b〉 Finite non-commutative monoid with 9 elements 20 isomorphic
10 〈a, b | aab=aaa, baa=b〉 Finite non-commutative monoid with 9 elements 1 isomorphic
10 〈a, b | aab=aaa, bbb=a〉 Finite commutative monoid with 9 elements 1 isomorphic
10 〈a, b | abb=aaa, bbb=a〉 Finite commutative monoid with 9 elements 12 isomorphic
10 〈a, b | aaa=aa, abbb=b〉 Finite non-commutative monoid with 9 elements 3 isomorphic
10 〈a, b | aaa=bb, aaba=b〉 Finite commutative monoid with 9 elements
10 〈a, b | aab=aa, bbbb=a〉 Finite commutative monoid with 9 elements 5 isomorphic
10 〈a, b | aaa=bb, aab=ab〉 Finite non-commutative monoid with 9 elements 1 isomorphic
10 〈a, b | aaa=a, ababa=b〉 Finite non-commutative monoid with 9 elements
10 〈a, b | aab=a, baaaa=b〉 Finite non-commutative monoid with 9 elements
10 〈a, b | aba=a, aaaab=b〉 Finite non-commutative monoid with 9 elements
10 〈a, b | aab=b, bbb=aaa〉 Finite commutative monoid with 9 elements 1 isomorphic
10 〈a, b | bb=aa, aaaa=ab〉 Finite non-commutative monoid with 9 elements 2 isomorphic
10 〈a, b | bb=aa, aabb=ba〉 Finite non-commutative monoid with 9 elements
10 〈a, b | ab=a, baaa=bbb〉 Finite non-commutative monoid with 9 elements 3 isomorphic
10 〈a, b | ab=a, bbaa=bbb〉 Finite non-commutative monoid with 9 elements 2 isomorphic
11 〈a, b | aba=aaa, aaab=b〉 Finite non-commutative monoid with 9 elements 3 isomorphic
11 〈a, b | abb=aaa, aaab=b〉 Finite commutative monoid with 9 elements 7 isomorphic
11 〈a, b | aaab=a, baaaa=b〉 Finite non-commutative monoid with 9 elements 1 isomorphic
11 〈a, b | aab=b, aaaaa=ba〉 Finite non-commutative monoid with 9 elements
11 〈a, b | aab=b, aaaaa=bb〉 Finite commutative monoid with 9 elements
11 〈a, b | aab=b, abaa=aaa〉 Finite non-commutative monoid with 9 elements
11 〈a, b | aab=b, babb=aaa〉 Finite commutative monoid with 9 elements 3 isomorphic
11 〈a, b | aba=a, abab=bbb〉 Finite non-commutative monoid with 9 elements
11 〈a, b | ab=aa, aaaaa=bb〉 Finite non-commutative monoid with 9 elements 15 isomorphic
11 〈a, b | ab=a, bbbbb=baa〉 Finite non-commutative monoid with 9 elements

Other isomorphic instances

40 total

Length:Presentation:
9〈a, b | aab=a, bbbb=a〉
9〈a, b | aba=a, bbbb=a〉
10〈a, b | aa=b, abbbb=bb〉
10〈a, b | aa=b, babbb=bb〉
10〈a, b | aa=b, bbabb=bb〉
11〈a, b | aaaa=ab, aabb=b〉
11〈a, b | aaaa=ab, abab=b〉
11〈a, b | aaaa=ab, abba=b〉
11〈a, b | aaa=b, aaabb=ab〉
11〈a, b | aaa=b, aaabb=ba〉
11〈a, b | aaa=b, aabab=ab〉
11〈a, b | aaa=b, aabab=ba〉
11〈a, b | aaa=b, aabba=ab〉
11〈a, b | aaa=b, aabba=ba〉
11〈a, b | aaa=b, abaab=ab〉
11〈a, b | aaa=b, abaab=ba〉
11〈a, b | aaa=b, ababa=ab〉
11〈a, b | aaa=b, baaab=ab〉
11〈a, b | aaa=b, aaaa=bbb〉
11〈a, b | aab=a, bbbb=aab〉
11〈a, b | aab=a, bbbb=aba〉
11〈a, b | aba=a, bbbb=aba〉
11〈a, b | aa=b, aaabbb=bb〉
11〈a, b | aa=b, aababb=bb〉
11〈a, b | aa=b, aabbab=bb〉
11〈a, b | aa=b, aabbba=bb〉
11〈a, b | aa=b, abaabb=bb〉
11〈a, b | aa=b, ababab=bb〉
11〈a, b | aa=b, ababba=bb〉
11〈a, b | aa=b, abbaab=bb〉
11〈a, b | aa=b, baaabb=bb〉
11〈a, b | aa=b, baabab=bb〉
11〈a, b | aa=b, abbbb=aab〉
11〈a, b | aa=b, abbbb=aba〉
11〈a, b | aa=b, abbbb=baa〉
11〈a, b | aa=b, babbb=aab〉
11〈a, b | aa=b, babbb=aba〉
11〈a, b | aa=b, babbb=baa〉
11〈a, b | aa=b, bbabb=aab〉
11〈a, b | aa=b, bbabb=aba〉