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〈a, b | aa=1, abbbb=b〉

Monoid presentation of length 8

Properties

Completion parameters

Complete rewriting system

  1. b7 ⇒ b
  2. ab ⇒ b4
  3. a2 ⇒ 1

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1abbab2b2ab3b3ab4b4ab5b5ab6b6a
11abbab2b2ab3b3ab4b4ab5b5ab6b6a
aa1b4b4ab5b5ab6b6abbab2b2ab3b3a
bbbab2b2ab3b3ab4b4ab5b5ab6b6abba
bababb5b5ab6b6abbab2b2ab3b3ab4b4a
b2b2b2ab3b3ab4b4ab5b5ab6b6abbab2b2a
b2ab2ab2b6b6abbab2b2ab3b3ab4b4ab5b5a
b3b3b3ab4b4ab5b5ab6b6abbab2b2ab3b3a
b3ab3ab3bbab2b2ab3b3ab4b4ab5b5ab6b6a
b4b4b4ab5b5ab6b6abbab2b2ab3b3ab4b4a
b4ab4ab4b2b2ab3b3ab4b4ab5b5ab6b6abba
b5b5b5ab6b6abbab2b2ab3b3ab4b4ab5b5a
b5ab5ab5b3b3ab4b4ab5b5ab6b6abbab2b2a
b6b6b6abbab2b2ab3b3ab4b4ab5b5ab6b6a
b6ab6ab6b4b4ab5b5ab6b6abbab2b2ab3b3a

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

35 unique, 295 total

Length:Presentation:Description:Related:
9 〈a, b | aba=bb, bab=a〉 Finite non-commutative monoid with 14 elements 1 isomorphic
9 〈a, b | aa=a, bbbb=ab〉 Finite non-commutative monoid with 14 elements 2 isomorphic
9 〈a, b | aa=1, ababbb=b〉 Finite non-commutative monoid with 14 elements 27 isomorphic, 10 anti-isomorphic
10 〈a, b | aaaa=bb, abbb=1〉 Isomorphic to ℤ14 165 isomorphic
10 〈a, b | aab=bb, bbba=a〉 Finite non-commutative monoid with 14 elements 5 isomorphic
10 〈a, b | aab=bb, aba=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
10 〈a, b | aab=b, bbba=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaaa=ab, baab=b〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | aaaa=bb, abbb=a〉 Finite commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aaaa=bb, abbb=b〉 Finite commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aabb=aa, baab=b〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | abab=aa, abba=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | abab=aa, baaa=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaaa=b, aabbb=a〉 Finite commutative monoid with 14 elements 15 isomorphic
11 〈a, b | aaaa=b, aabbb=b〉 Finite commutative monoid with 14 elements 5 isomorphic
11 〈a, b | aaa=bb, abbbb=b〉 Finite commutative monoid with 14 elements 11 isomorphic
11 〈a, b | aaa=bb, babbb=a〉 Finite commutative monoid with 14 elements
11 〈a, b | aab=aa, baaaa=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaa=ab, baab=bb〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aaa=bb, bbbb=ab〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aab=bb, abab=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aba=bb, bbbb=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aab=b, abbaa=aa〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | aab=b, babba=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aab=a, bbbb=baa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | ab=aa, bbbbb=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbbb=ba〉 Finite non-commutative monoid with 14 elements
11 〈a, b | ab=aa, bbaa=bbb〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbb=aaa〉 Finite non-commutative monoid with 14 elements 3 isomorphic
11 〈a, b | ab=aa, bbbb=baa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbb=bba〉 Finite non-commutative monoid with 14 elements
11 〈a, b | bb=aa, abab=aaa〉 Finite non-commutative monoid with 14 elements 2 anti-isomorphic
11 〈a, b | aa=a, bbbbbbb=a〉 Finite commutative monoid with 14 elements
11 〈a, b | aa=b, bbbbbbb=b〉 Finite commutative monoid with 14 elements
11 〈a, b | ab=a, bbaaaa=bb〉 Finite non-commutative monoid with 14 elements

Other isomorphic instances

14 total

Length:Presentation:
8〈a, b | aa=1, bbbb=ab〉
10〈a, b | aa=1, aaabbbb=b〉
10〈a, b | aa=1, abaabbb=b〉
10〈a, b | aa=1, ababbab=b〉
10〈a, b | aa=1, abbaabb=b〉
10〈a, b | aa=1, abbabab=b〉
10〈a, b | aa=1, abbbaab=b〉
10〈a, b | aa=1, aabbbb=ab〉
10〈a, b | aa=1, baabbb=ab〉
10〈a, b | aa=1, babbab=ab〉
10〈a, b | aa=1, bbaabb=ab〉
10〈a, b | aa=1, abbbb=aab〉
10〈a, b | aa=1, abbbb=baa〉
10〈a, b | aa=1, bbbb=aaab〉

Other anti-isomorphic instances

7 total

Length:Presentation:
10〈a, b | aa=1, aabbbba=b〉
10〈a, b | aa=1, aabbbb=ba〉
10〈a, b | aa=1, abbbba=ab〉
10〈a, b | aa=1, baabbb=ba〉
10〈a, b | aa=1, bababb=ba〉
10〈a, b | aa=1, abbbb=aba〉
10〈a, b | aa=1, bbbb=aaba〉