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〈a, b | ab=a, bb=aa〉

Monoid presentation of length 7

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ a
  2. ba ⇒ a
  3. b2 ⇒ a2
  4. a3 ⇒ a

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2
11aba2
aaa2aa
bbaa2a2
a2a2aa2a2

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

8 unique, 1590 total

Length:Presentation:Description:Related:
5 〈a, b | aa=b, bb=1〉 Isomorphic to ℤ4 1419 isomorphic
6 〈a, b | aa=a, bb=a〉 Finite commutative monoid with 4 elements 37 isomorphic
6 〈a, b | aa=b, bb=a〉 Finite commutative monoid with 4 elements 72 isomorphic
7 〈a, b | ab=aa, ba=b〉 Finite non-commutative monoid with 4 elements 8 isomorphic, 6 anti-isomorphic
7 〈a, b | ab=aa, bb=a〉 Finite commutative monoid with 4 elements 16 isomorphic
7 〈a, b | aa=a, abb=b〉 Finite non-commutative monoid with 4 elements 14 isomorphic
9 〈a, b | aa=a, abbba=b〉 Finite commutative monoid with 4 elements 8 isomorphic
10 〈a, b | aaa=aa, abba=b〉 Finite commutative monoid with 4 elements 2 isomorphic

Other isomorphic instances

17 total

Length:Presentation:
8〈a, b | ab=a, aab=bb〉
8〈a, b | ab=a, aba=bb〉
9〈a, b | ab=a, aabb=bb〉
9〈a, b | ab=a, abab=bb〉
9〈a, b | ab=a, abba=bb〉
10〈a, b | ab=a, aabbb=bb〉
10〈a, b | ab=a, ababb=bb〉
10〈a, b | ab=a, abbab=bb〉
10〈a, b | ab=a, abbba=bb〉
11〈a, b | aabb=aa, abbb=b〉
11〈a, b | abab=aa, abbb=b〉
11〈a, b | abba=bb, baaa=a〉
11〈a, b | ab=a, aabbbb=bb〉
11〈a, b | ab=a, ababbb=bb〉
11〈a, b | ab=a, abbabb=bb〉
11〈a, b | ab=a, abbbab=bb〉
11〈a, b | ab=a, abbbba=bb〉