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〈a, b | bb=aa, aaaba=b〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. b9 ⇒ b
  2. ba ⇒ ab5
  3. a2 ⇒ b2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8
11ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8
aab2abb3ab2b4ab3b5ab4b6ab5b7ab6b8ab7bab8b2
bbab5b2ab6b3ab7b4ab8b5abb6ab2b7ab3b8ab4bab5
ababb7ab2b8ab3bab4b2ab5b3ab6b4ab7b5ab8b6abb7
b2b2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8babb2ab2
ab2ab2b4ab3b5ab4b6ab5b7ab6b8ab7bab8b2abb3ab2b4
b3b3ab7b4ab8b5abb6ab2b7ab3b8ab4bab5b2ab6b3ab7
ab3ab3bab4b2ab5b3ab6b4ab7b5ab8b6abb7ab2b8ab3b
b4b4ab4b5ab5b6ab6b7ab7b8ab8babb2ab2b3ab3b4ab4
ab4ab4b6ab5b7ab6b8ab7bab8b2abb3ab2b4ab3b5ab4b6
b5b5abb6ab2b7ab3b8ab4bab5b2ab6b3ab7b4ab8b5ab
ab5ab5b3ab6b4ab7b5ab8b6abb7ab2b8ab3bab4b2ab5b3
b6b6ab6b7ab7b8ab8babb2ab2b3ab3b4ab4b5ab5b6ab6
ab6ab6b8ab7bab8b2abb3ab2b4ab3b5ab4b6ab5b7ab6b8
b7b7ab3b8ab4bab5b2ab6b3ab7b4ab8b5abb6ab2b7ab3
ab7ab7b5ab8b6abb7ab2b8ab3bab4b2ab5b3ab6b4ab7b5
b8b8ab8babb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8
ab8ab8b2abb3ab2b4ab3b5ab4b6ab5b7ab6b8ab7bab8b2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

18 unique, 102 total

Length:Presentation:Description:Related:
8 〈a, b | aa=1, abbba=b〉 Finite non-commutative monoid with 18 elements 14 isomorphic
9 〈a, b | aa=1, abbbbb=b〉 Finite non-commutative monoid with 18 elements 22 isomorphic, 9 anti-isomorphic
10 〈a, b | aaab=1, bbbbbb=1〉 Isomorphic to ℤ18 33 isomorphic
10 〈a, b | aba=a, aaab=bb〉 Finite non-commutative monoid with 18 elements
10 〈a, b | aba=b, baab=aa〉 Finite non-commutative monoid with 18 elements
10 〈a, b | aba=b, bbbb=aa〉 Finite non-commutative monoid with 18 elements
10 〈a, b | aa=a, bbbbb=ab〉 Finite non-commutative monoid with 18 elements 1 isomorphic
10 〈a, b | aa=1, abababa=b〉 Finite non-commutative monoid with 18 elements 2 isomorphic
11 〈a, b | aaaa=ab, babb=b〉 Finite non-commutative monoid with 18 elements 2 isomorphic
11 〈a, b | aab=bb, bbbba=a〉 Finite non-commutative monoid with 18 elements
11 〈a, b | aaa=ab, bbbb=ab〉 Finite non-commutative monoid with 18 elements
11 〈a, b | aaa=ab, bbbb=ba〉 Finite non-commutative monoid with 18 elements
11 〈a, b | aab=bb, baba=aa〉 Finite non-commutative monoid with 18 elements
11 〈a, b | aaa=a, bbbbbb=a〉 Finite commutative monoid with 18 elements
11 〈a, b | aaa=b, bbbbbb=a〉 Finite commutative monoid with 18 elements
11 〈a, b | aaa=b, bbbbbb=b〉 Finite commutative monoid with 18 elements
11 〈a, b | aab=b, bbbba=aa〉 Finite non-commutative monoid with 18 elements
11 〈a, b | bb=aa, ababa=aa〉 Finite non-commutative monoid with 18 elements 1 isomorphic

Other isomorphic instances

2 total

Length:Presentation:
10〈a, b | bb=aa, aabab=a〉
10〈a, b | bb=aa, abbba=b〉