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〈a, b | aabb=aa, baab=b〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a6 ⇒ a2
  2. ba4 ⇒ b
  3. a2b ⇒ a4
  4. b2 ⇒ ba2
  5. bab ⇒ ba3

Idempotents

4 elements

Cayley table

Idempotents are shown in bold.

1aba2abbaa3ababa2a4aba2ba3a5aba3
11aba2abbaa3ababa2a4aba2ba3a5aba3
aaa2aba3a4abaa4a5aba2a5a2aba3a2a3
bbbaba2ba2ba3ba3ba3bbbbabababa2
a2a2a3a4a4a5a5a5a2a2a2a3a3a3a4
abababaaba2aba2aba3aba3aba3ababababaabaabaaba2
bababa2ba3ba3bbbbabababa2ba2ba2ba3
a3a3a4a5a5a2a2a2a3a3a3a4a4a4a5
abaabaaba2aba3aba3ababababaabaabaaba2aba2aba2aba3
ba2ba2ba3bbbabababa2ba2ba2ba3ba3ba3b
a4a4a5a2a2a3a3a3a4a4a4a5a5a5a2
aba2aba2aba3abababaabaabaaba2aba2aba2aba3aba3aba3ab
ba3ba3bbababa2ba2ba2ba3ba3ba3bbbba
a5a5a2a3a3a4a4a4a5a5a5a2a2a2a3
aba3aba3ababaabaaba2aba2aba2aba3aba3aba3ababababa

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

35 unique, 314 total

Length:Presentation:Description:Related:
8 〈a, b | aa=1, abbbb=b〉 Finite non-commutative monoid with 14 elements 14 isomorphic, 7 anti-isomorphic
9 〈a, b | aba=bb, bab=a〉 Finite non-commutative monoid with 14 elements 1 isomorphic
9 〈a, b | aa=a, bbbb=ab〉 Finite non-commutative monoid with 14 elements 2 isomorphic
9 〈a, b | aa=1, ababbb=b〉 Finite non-commutative monoid with 14 elements 27 isomorphic, 10 anti-isomorphic
10 〈a, b | aaaa=bb, abbb=1〉 Isomorphic to ℤ14 165 isomorphic
10 〈a, b | aab=bb, bbba=a〉 Finite non-commutative monoid with 14 elements 5 isomorphic
10 〈a, b | aab=bb, aba=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
10 〈a, b | aab=b, bbba=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaaa=ab, baab=b〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | aaaa=bb, abbb=a〉 Finite commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aaaa=bb, abbb=b〉 Finite commutative monoid with 14 elements 1 isomorphic
11 〈a, b | abab=aa, abba=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | abab=aa, baaa=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaaa=b, aabbb=a〉 Finite commutative monoid with 14 elements 15 isomorphic
11 〈a, b | aaaa=b, aabbb=b〉 Finite commutative monoid with 14 elements 5 isomorphic
11 〈a, b | aaa=bb, abbbb=b〉 Finite commutative monoid with 14 elements 11 isomorphic
11 〈a, b | aaa=bb, babbb=a〉 Finite commutative monoid with 14 elements
11 〈a, b | aab=aa, baaaa=b〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aaa=ab, baab=bb〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aaa=bb, bbbb=ab〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aab=bb, abab=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aba=bb, bbbb=aa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | aab=b, abbaa=aa〉 Finite non-commutative monoid with 14 elements 2 isomorphic
11 〈a, b | aab=b, babba=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | aab=a, bbbb=baa〉 Finite non-commutative monoid with 14 elements
11 〈a, b | ab=aa, bbbbb=aa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbbb=ba〉 Finite non-commutative monoid with 14 elements
11 〈a, b | ab=aa, bbaa=bbb〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbb=aaa〉 Finite non-commutative monoid with 14 elements 3 isomorphic
11 〈a, b | ab=aa, bbbb=baa〉 Finite non-commutative monoid with 14 elements 1 isomorphic
11 〈a, b | ab=aa, bbbb=bba〉 Finite non-commutative monoid with 14 elements
11 〈a, b | bb=aa, abab=aaa〉 Finite non-commutative monoid with 14 elements 2 anti-isomorphic
11 〈a, b | aa=a, bbbbbbb=a〉 Finite commutative monoid with 14 elements
11 〈a, b | aa=b, bbbbbbb=b〉 Finite commutative monoid with 14 elements
11 〈a, b | ab=a, bbaaaa=bb〉 Finite non-commutative monoid with 14 elements

Other isomorphic instances

2 total

Length:Presentation:
11〈a, b | aabb=aa, baba=b〉
11〈a, b | aabb=aa, bbaa=b〉