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〈a, b | ab=a, aaaa=bbb〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a5 ⇒ a
  2. ba ⇒ a
  3. ab ⇒ a
  4. b3 ⇒ a4

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2b2a3a4
11aba2b2a3a4
aaa2aa3aa4a
bbab2a2a4a3a4
a2a2a3a2a4a2aa2
b2b2aa4a2a4a3a4
a3a3a4a3aa3a2a3
a4a4aa4a2a4a3a4

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

32 unique, 1219 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
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, 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

4 total

Length:Presentation:
11〈a, b | ab=a, aaaab=bbb〉
11〈a, b | ab=a, aaaba=bbb〉
11〈a, b | ab=a, aabaa=bbb〉
11〈a, b | ab=a, abaaa=bbb〉