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〈a, b | aba=aa, bbbb=ab〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b8 ⇒ b7
  2. ab ⇒ b4
  3. a2 ⇒ b4a

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1abbab2b2ab3b3ab4b4ab5b5ab6b6ab7b7a
11abbab2b2ab3b3ab4b4ab5b5ab6b6ab7b7a
aab4ab4b4ab5b5ab6b6ab7b7ab7b7ab7b7ab7b7a
bbbab2b2ab3b3ab4b4ab5b5ab6b6ab7b7ab7b7a
babab5ab5b5ab6b6ab7b7ab7b7ab7b7ab7b7ab7b7a
b2b2b2ab3b3ab4b4ab5b5ab6b6ab7b7ab7b7ab7b7a
b2ab2ab6ab6b6ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7a
b3b3b3ab4b4ab5b5ab6b6ab7b7ab7b7ab7b7ab7b7a
b3ab3ab7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7a
b4b4b4ab5b5ab6b6ab7b7ab7b7ab7b7ab7b7ab7b7a
b4ab4ab7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7a
b5b5b5ab6b6ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7a
b5ab5ab7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7a
b6b6b6ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7a
b6ab6ab7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7a
b7b7b7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7a
b7ab7ab7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7ab7b7a

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 | 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 | 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