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〈a, b | bab=aba, bbb=aa〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b8 ⇒ b7
  2. ab4 ⇒ b7
  3. bab2 ⇒ b7
  4. b2ab ⇒ b7
  5. b3a ⇒ ab3
  6. a2 ⇒ b3
  7. aba ⇒ bab

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1ababbab2ab2babb2ab3ab2aab3b4b5b6b7
11ababbab2ab2babb2ab3ab2aab3b4b5b6b7
aab3abb4babab2b5b7ab2aab3b7b6b7b7b7b7
bbbab2babb2ab3b7b7ab3b4b7b7b5b6b7b7
ababbabab2b7ab2aab3b7b7b6b7b7b7b7b7b7b7
babab4babb5b7b7b6b7b7b7b7b7b7b7b7b7
b2b2b2ab3b7ab3b4b7b7b7b5b7b7b6b7b7b7
ab2ab2ab2aab3b7b6b7b7b7b7b7b7b7b7b7b7b7
babbabb7b7b7b7b7b7b7b7b7b7b7b7b7b7b7
b2ab2ab5b7b6b7b7b7b7b7b7b7b7b7b7b7b7
b3b3ab3b4b7b7b5b7b7b7b6b7b7b7b7b7b7
ab2aab2ab7b7b7b7b7b7b7b7b7b7b7b7b7b7b7
ab3ab3b6b7b7b7b7b7b7b7b7b7b7b7b7b7b7
b4b4b7b5b7b7b6b7b7b7b7b7b7b7b7b7b7
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=aab, 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