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〈a, b | ab=a, baaaa=b〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ a
  2. b2 ⇒ b
  3. a5 ⇒ a
  4. ba4 ⇒ b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3
11aba2baa3ba2a4ba3
aaa2aa3a2a4a3aa4
bbbabba2baba3ba2bba3
a2a2a3a2a4a3aa4a2a
bababa2baba3ba2bba3bab
a3a3a4a3aa4a2aa3a2
ba2ba2ba3ba2bba3babba2ba
a4a4aa4a2aa3a2a4a3
ba3ba3bba3babba2baba3ba2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

38 unique, 922 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=ab, bbb=a〉 Finite commutative monoid with 9 elements 40 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
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

20 total

Length:Presentation:
10〈a, b | ab=a, baaaab=b〉
10〈a, b | ab=a, baaaba=b〉
10〈a, b | ab=a, baabaa=b〉
10〈a, b | ab=a, babaaa=b〉
10〈a, b | ab=a, bbaaaa=b〉
11〈a, b | ab=a, baaaabb=b〉
11〈a, b | ab=a, baaabab=b〉
11〈a, b | ab=a, baaabba=b〉
11〈a, b | ab=a, baabaab=b〉
11〈a, b | ab=a, baababa=b〉
11〈a, b | ab=a, baabbaa=b〉
11〈a, b | ab=a, babaaab=b〉
11〈a, b | ab=a, babaaba=b〉
11〈a, b | ab=a, bababaa=b〉
11〈a, b | ab=a, babbaaa=b〉
11〈a, b | ab=a, bbaaaab=b〉
11〈a, b | ab=a, bbaaaba=b〉
11〈a, b | ab=a, bbaabaa=b〉
11〈a, b | ab=a, bbabaaa=b〉
11〈a, b | ab=a, bbbaaaa=b〉