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〈a, b | ab=a, bbbb=baaa〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ a
  2. b2a ⇒ ba
  3. a4 ⇒ a
  4. b4 ⇒ ba3

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b3ba3
11aba2bab2a3ba2b3ba3
aaa2aa3a2aaa3aa
bbbab2ba2bab3ba3ba2ba3ba3
a2a2a3a2aa3a2a2aa2a2
bababa2baba3ba2bababa3baba
b2b2bab3ba2baba3ba3ba2ba3ba3
a3a3aa3a2aa3a3a2a3a3
ba2ba2ba3ba2baba3ba2ba2baba2ba2
b3b3baba3ba2baba3ba3ba2ba3ba3
ba3ba3baba3ba2baba3ba3ba2ba3ba3

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

37 unique, 919 total

Length:Presentation:Description:Related:
7 〈a, b | aa=1, abbb=b〉 Finite non-commutative monoid with 10 elements 51 isomorphic, 34 anti-isomorphic
8 〈a, b | aaa=b, abbb=1〉 Isomorphic to ℤ10 536 isomorphic
8 〈a, b | bb=aa, aba=a〉 Finite non-commutative monoid with 10 elements 1 isomorphic
8 〈a, b | bb=aa, aba=b〉 Finite non-commutative monoid with 10 elements 1 isomorphic
8 〈a, b | aa=a, bbb=ab〉 Finite non-commutative monoid with 10 elements 3 isomorphic
9 〈a, b | aab=bb, bba=a〉 Finite non-commutative monoid with 10 elements 6 isomorphic
9 〈a, b | aaa=b, abbb=a〉 Finite commutative monoid with 10 elements 59 isomorphic
9 〈a, b | aaa=b, abbb=b〉 Finite commutative monoid with 10 elements 35 isomorphic
9 〈a, b | bb=aa, aba=aa〉 Finite non-commutative monoid with 10 elements 1 isomorphic
9 〈a, b | aa=a, bbbbb=a〉 Finite commutative monoid with 10 elements 17 isomorphic
9 〈a, b | aa=b, bbbbb=b〉 Finite commutative monoid with 10 elements 57 isomorphic
10 〈a, b | aaaa=b, aabb=b〉 Finite commutative monoid with 10 elements 20 isomorphic
10 〈a, b | aaa=bb, abb=ab〉 Finite non-commutative monoid with 10 elements 2 isomorphic
10 〈a, b | aaa=bb, abb=ba〉 Finite non-commutative monoid with 10 elements
10 〈a, b | aab=aa, aba=bb〉 Finite non-commutative monoid with 10 elements
10 〈a, b | aaa=b, abbb=bb〉 Finite commutative monoid with 10 elements 3 isomorphic
10 〈a, b | aab=a, baaa=bb〉 Finite non-commutative monoid with 10 elements
10 〈a, b | ab=aa, baaaa=b〉 Finite non-commutative monoid with 10 elements 14 isomorphic
10 〈a, b | ab=aa, baaa=bb〉 Finite non-commutative monoid with 10 elements 3 isomorphic
10 〈a, b | aa=a, abbbbb=b〉 Finite non-commutative monoid with 10 elements 5 isomorphic
10 〈a, b | ab=a, baaaa=bb〉 Finite non-commutative monoid with 10 elements 4 isomorphic
11 〈a, b | aaab=baa, abab=1〉 Finite non-Abelian group with 10 elements 3 isomorphic
11 〈a, b | aaaa=aa, abba=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aaaa=ab, baaa=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aaaa=bb, aaab=a〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aaaa=bb, aaab=b〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aabb=aa, bbbb=a〉 Finite commutative monoid with 10 elements 3 isomorphic
11 〈a, b | abab=aa, baab=b〉 Finite non-commutative monoid with 10 elements 4 isomorphic
11 〈a, b | aab=bb, aaaaa=b〉 Finite commutative monoid with 10 elements 7 isomorphic
11 〈a, b | aab=bb, abbbb=a〉 Finite commutative monoid with 10 elements 5 isomorphic
11 〈a, b | aba=aa, aaaab=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aab=b, abbbb=aa〉 Finite commutative monoid with 10 elements 5 isomorphic
11 〈a, b | aaa=b, abbb=bbb〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aab=a, bbbb=bab〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aab=b, aaaa=baa〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aba=b, aaaa=bbb〉 Finite commutative monoid with 10 elements
11 〈a, b | ab=a, bbbb=bbaa〉 Finite non-commutative monoid with 10 elements