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〈a, b | ab=aa, bbba=bbb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ a2
  2. b3a ⇒ b3
  3. b4 ⇒ b3
  4. a5 ⇒ a4

Idempotents

5 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2ab3a4ba3b2a2ba4b2a3b2a4
11aba2bab2a3ba2b2ab3a4ba3b2a2ba4b2a3b2a4
aaa2a2a3a3a3a4a4a4a4a4a4a4a4a4a4
bbbab2ba2b2ab3ba3b2a2b3b3ba4b2a3b3b2a4b3b3
a2a2a3a3a4a4a4a4a4a4a4a4a4a4a4a4a4
bababa2ba2ba3ba3ba3ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4
b2b2b2ab3b2a2b3b3b2a3b3b3b3b2a4b3b3b3b3b3
a3a3a4a4a4a4a4a4a4a4a4a4a4a4a4a4a4
ba2ba2ba3ba3ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4
b2ab2ab2a2b2a2b2a3b2a3b2a3b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4
b3b3b3b3b3b3b3b3b3b3b3b3b3b3b3b3b3
a4a4a4a4a4a4a4a4a4a4a4a4a4a4a4a4a4
ba3ba3ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4
b2a2b2a2b2a3b2a3b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4
ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4ba4
b2a3b2a3b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4
b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4b2a4

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 | 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 | aa=a, ababab=bb〉 Finite non-commutative monoid with 16 elements