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〈a, b | ab=a, baaa=b〉

Monoid presentation of length 8

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ a
  2. b2 ⇒ b
  3. a4 ⇒ a
  4. ba3 ⇒ b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2
11aba2baa3ba2
aaa2aa3a2aa3
bbbabba2babba2
a2a2a3a2aa3a2a
bababa2babba2bab
a3a3aa3a2aa3a2
ba2ba2bba2babba2ba

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

32 unique, 1189 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
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

34 total

Length:Presentation:
9〈a, b | ab=a, baaab=b〉
9〈a, b | ab=a, baaba=b〉
9〈a, b | ab=a, babaa=b〉
9〈a, b | ab=a, bbaaa=b〉
10〈a, b | ab=a, baaabb=b〉
10〈a, b | ab=a, baabab=b〉
10〈a, b | ab=a, baabba=b〉
10〈a, b | ab=a, babaab=b〉
10〈a, b | ab=a, bababa=b〉
10〈a, b | ab=a, babbaa=b〉
10〈a, b | ab=a, bbaaab=b〉
10〈a, b | ab=a, bbaaba=b〉
10〈a, b | ab=a, bbabaa=b〉
10〈a, b | ab=a, bbbaaa=b〉
11〈a, b | ab=a, baaabbb=b〉
11〈a, b | ab=a, baababb=b〉
11〈a, b | ab=a, baabbab=b〉
11〈a, b | ab=a, baabbba=b〉
11〈a, b | ab=a, babaabb=b〉
11〈a, b | ab=a, bababab=b〉
11〈a, b | ab=a, bababba=b〉
11〈a, b | ab=a, babbaab=b〉
11〈a, b | ab=a, babbaba=b〉
11〈a, b | ab=a, babbbaa=b〉
11〈a, b | ab=a, bbaaabb=b〉
11〈a, b | ab=a, bbaabab=b〉
11〈a, b | ab=a, bbaabba=b〉
11〈a, b | ab=a, bbabaab=b〉
11〈a, b | ab=a, bbababa=b〉
11〈a, b | ab=a, bbabbaa=b〉
11〈a, b | ab=a, bbbaaab=b〉
11〈a, b | ab=a, bbbaaba=b〉
11〈a, b | ab=a, bbbabaa=b〉
11〈a, b | ab=a, bbbbaaa=b〉