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〈a, b | ab=a, aaa=bb〉

Monoid presentation of length 8

Properties

Completion parameters

Complete rewriting system

  1. a4 ⇒ a
  2. ba ⇒ a
  3. ab ⇒ a
  4. b2 ⇒ a3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2a3
11aba2a3
aaa2aa3a
bbaa3a2a3
a2a2a3a2aa2
a3a3aa3a2a3

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

16 unique, 1443 total

Length:Presentation:Description:Related:
6 〈a, b | aa=b, abb=1〉 Isomorphic to ℤ5 1132 isomorphic
7 〈a, b | aa=b, abb=a〉 Finite commutative monoid with 5 elements 71 isomorphic
7 〈a, b | aa=b, abb=b〉 Finite commutative monoid with 5 elements 43 isomorphic
7 〈a, b | ab=a, baa=b〉 Finite non-commutative monoid with 5 elements 43 isomorphic
8 〈a, b | aaa=b, aab=b〉 Finite commutative monoid with 5 elements 27 isomorphic
8 〈a, b | aab=a, baa=b〉 Finite non-commutative monoid with 5 elements 8 isomorphic
8 〈a, b | aab=b, aba=a〉 Finite non-commutative monoid with 5 elements 8 isomorphic
8 〈a, b | ab=a, bbbb=a〉 Finite commutative monoid with 5 elements 32 isomorphic
8 〈a, b | ab=a, bba=bb〉 Finite non-commutative monoid with 5 elements 15 isomorphic
8 〈a, b | ab=a, bbb=aa〉 Finite commutative monoid with 5 elements 9 isomorphic
8 〈a, b | ab=a, bbb=ba〉 Finite non-commutative monoid with 5 elements 4 isomorphic
9 〈a, b | aab=aa, bba=b〉 Finite non-commutative monoid with 5 elements 9 isomorphic
9 〈a, b | aab=b, aaba=a〉 Finite non-commutative monoid with 5 elements 10 isomorphic
10 〈a, b | aa=a, abbbba=b〉 Finite commutative monoid with 5 elements 3 isomorphic
11 〈a, b | aabb=a, baabb=b〉 Finite non-commutative monoid with 5 elements 10 isomorphic, 3 anti-isomorphic
11 〈a, b | aaa=aa, abbba=b〉 Finite commutative monoid with 5 elements

Other isomorphic instances

19 total

Length:Presentation:
9〈a, b | ab=a, aaab=bb〉
9〈a, b | ab=a, aaba=bb〉
9〈a, b | ab=a, abaa=bb〉
10〈a, b | ab=a, aaabb=bb〉
10〈a, b | ab=a, aabab=bb〉
10〈a, b | ab=a, aabba=bb〉
10〈a, b | ab=a, abaab=bb〉
10〈a, b | ab=a, ababa=bb〉
10〈a, b | ab=a, abbaa=bb〉
11〈a, b | ab=a, aaabbb=bb〉
11〈a, b | ab=a, aababb=bb〉
11〈a, b | ab=a, aabbab=bb〉
11〈a, b | ab=a, aabbba=bb〉
11〈a, b | ab=a, abaabb=bb〉
11〈a, b | ab=a, ababab=bb〉
11〈a, b | ab=a, ababba=bb〉
11〈a, b | ab=a, abbaab=bb〉
11〈a, b | ab=a, abbaba=bb〉
11〈a, b | ab=a, abbbaa=bb〉