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〈a, b | ab=a, bbb=baa〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ a
  2. a3 ⇒ a
  3. b2a ⇒ ba
  4. b3 ⇒ ba2

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2ba2
11aba2bab2ba2
aaa2aaa2aa
bbbab2ba2baba2ba2
a2a2aa2a2aa2a2
bababa2bababa2baba
b2b2baba2ba2baba2ba2
ba2ba2baba2ba2baba2ba2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

32 unique, 1218 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 | 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
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

5 total

Length:Presentation:
10〈a, b | ab=a, baab=bbb〉
10〈a, b | ab=a, baba=bbb〉
11〈a, b | ab=a, baabb=bbb〉
11〈a, b | ab=a, babab=bbb〉
11〈a, b | ab=a, babba=bbb〉