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〈a, b | bab=aab, bbb=aa〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b8 ⇒ b7
  2. ab4 ⇒ b6
  3. bab ⇒ b4
  4. b3a ⇒ ab3
  5. a2 ⇒ b3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1ababbab2abaab2b2ab3ab2aab3b4b5b6b7
11ababbab2abaab2b2ab3ab2aab3b4b5b6b7
aab3abb4abaab2b6b5ab2aab3b7b6b6b7b7b7
bbbab2b4b2ab3b6b5ab3b4b7b6b5b6b7b7
abababaab2b6ab2aab3b7b7b6b6b7b7b7b7b7b7
babab4b4b5b6b5b7b6b7b6b7b7b7b7b7b7
b2b2b2ab3b5ab3b4b7b6b6b5b7b7b6b7b7b7
abaabab6b6b7b7b7b7b7b7b7b7b7b7b7b7b7
ab2ab2ab2aab3b7b6b6b7b7b7b7b7b7b7b7b7b7
b2ab2ab5b5b6b7b6b7b7b7b7b7b7b7b7b7b7
b3b3ab3b4b6b6b5b7b7b7b6b7b7b7b7b7b7
ab2aab2ab7b7b7b7b7b7b7b7b7b7b7b7b7b7b7
ab3ab3b6b6b7b7b7b7b7b7b7b7b7b7b7b7b7
b4b4b6b5b7b7b6b7b7b7b7b7b7b7b7b7b7
b5b5b7b6b7b7b7b7b7b7b7b7b7b7b7b7b7
b6b6b7b7b7b7b7b7b7b7b7b7b7b7b7b7b7
b7b7b7b7b7b7b7b7b7b7b7b7b7b7b7b7b7

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

26 unique, 175 total

Length:Presentation:Description:Related:
8 〈a, b | bb=aa, abab=1〉 Finite non-Abelian group with 16 elements 4 isomorphic
8 〈a, b | aa=1, ababbb=1〉 Finite non-Abelian group with 16 elements 40 isomorphic
9 〈a, b | aaaa=b, bbbb=1〉 Isomorphic to ℤ16 67 isomorphic
9 〈a, b | aab=a, bbbb=b〉 Finite non-commutative monoid with 16 elements
10 〈a, b | aaab=ba, abab=1〉 Finite non-Abelian group with 16 elements 7 isomorphic
10 〈a, b | bab=aaa, aabb=1〉 Finite non-Abelian group with 16 elements 6 isomorphic
10 〈a, b | aaaa=a, aabb=b〉 Finite non-commutative monoid with 16 elements 1 isomorphic
10 〈a, b | aaaa=a, bbbb=a〉 Finite commutative monoid with 16 elements 1 isomorphic
10 〈a, b | aaaa=b, bbbb=a〉 Finite commutative monoid with 16 elements 5 isomorphic
10 〈a, b | aba=b, aaaabb=1〉 Finite non-Abelian group with 16 elements 3 isomorphic
10 〈a, b | aba=b, aabbbb=1〉 Finite non-Abelian group with 16 elements 5 isomorphic
11 〈a, b | aaaa=aa, bbbb=a〉 Finite commutative monoid with 16 elements
11 〈a, b | aaaa=ab, bbbb=a〉 Finite commutative monoid with 16 elements 2 isomorphic
11 〈a, b | aaaa=bb, bbbb=a〉 Finite commutative monoid with 16 elements
11 〈a, b | aaab=bb, abba=a〉 Finite non-commutative monoid with 16 elements 2 isomorphic
11 〈a, b | bab=aba, bbb=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaaa=a, aabab=b〉 Finite non-commutative monoid with 16 elements 1 isomorphic
11 〈a, b | aab=bb, abbba=a〉 Finite non-commutative monoid with 16 elements 3 isomorphic
11 〈a, b | aaa=ab, babb=bb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=ab, bbaa=bb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=bb, abab=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aba=aa, bbbb=ab〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=b, abbbbb=b〉 Finite commutative monoid with 16 elements 2 isomorphic
11 〈a, b | aba=b, aaaa=abb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | ab=aa, bbba=bbb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aa=a, ababab=bb〉 Finite non-commutative monoid with 16 elements