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〈a, b | aab=b, babb=a〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. ba ⇒ ab
  2. a3 ⇒ a
  3. a2b ⇒ b
  4. b3 ⇒ a2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2abb2ab2
11aba2abb2ab2
aaa2ababab2b2
bbabb2bab2a2a
a2a2aba2abb2ab2
ababbab2abb2aa2
b2b2ab2a2b2abab
ab2ab2b2aab2a2abb

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

32 unique, 1203 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=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 | 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

20 total

Length:Presentation:
9〈a, b | aab=b, bbab=a〉
9〈a, b | aba=b, abbb=a〉
9〈a, b | aba=b, babb=a〉
11〈a, b | aab=b, aababb=a〉
11〈a, b | aab=b, aabbab=a〉
11〈a, b | aab=b, ababab=a〉
11〈a, b | aab=b, baaabb=a〉
11〈a, b | aab=b, baabab=a〉
11〈a, b | aab=b, babaab=a〉
11〈a, b | aab=b, bbaaab=a〉
11〈a, b | aba=b, aaabbb=a〉
11〈a, b | aba=b, aababb=a〉
11〈a, b | aba=b, aabbab=a〉
11〈a, b | aba=b, aabbba=a〉
11〈a, b | aba=b, abaabb=a〉
11〈a, b | aba=b, ababab=a〉
11〈a, b | aba=b, ababba=a〉
11〈a, b | aba=b, abbaab=a〉
11〈a, b | aba=b, baaabb=a〉
11〈a, b | aba=b, baabab=a〉