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〈a, b | aaba=b, babbb=a〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. ba ⇒ ab
  2. a4 ⇒ a
  3. a3b ⇒ b
  4. b4 ⇒ a3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2abb2a3a2bab2b3a2b2ab3a2b3
11aba2abb2a3a2bab2b3a2b2ab3a2b3
aaa2aba3a2bab2aba2b2ab3b2a2b3b3
bbabb2a2bab2b3ba2b2ab3a3a2b3aa2
a2a2a3a2baba2b2a2abb2a2b3ab2b3ab3
ababa2bab2ba2b2ab3abb2a2b3ab3a2a3
b2b2ab2b3a2b2ab3a3b2a2b3aba2aba2b
a3a3aba2abb2a3a2bab2b3a2b2ab3a2b3
a2ba2bba2b2abb2a2b3a2bab2b3a2ab3a3a
ab2ab2a2b2ab3b2a2b3aab2b3a2aba3a2bb
b3b3ab3a3a2b3abb3a2abb2a2bab2a2b2
a2b2a2b2b2a2b3ab2b3a2a2b2ab3a3a2babab
ab3ab3a2b3ab3a2abab3a3a2bab2ba2b2b2
a2b3a2b3b3a2ab3a3a2ba2b3aba2b2abb2ab2

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

33 unique, 301 total

Length:Presentation:Description:Related:
9 〈a, b | aaaa=b, abbb=1〉 Isomorphic to ℤ13 189 isomorphic
9 〈a, b | aba=b, baab=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
10 〈a, b | aaaa=b, abbb=a〉 Finite commutative monoid with 13 elements 10 isomorphic
10 〈a, b | aaaa=b, abbb=b〉 Finite commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaab=b, abba=a〉 Finite non-commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aaa=ab, babb=b〉 Finite non-commutative monoid with 13 elements 6 isomorphic
10 〈a, b | aaa=ab, bba=bb〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=ab, bbb=ab〉 Finite non-commutative monoid with 13 elements 1 isomorphic
10 〈a, b | aaa=ab, bbb=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=bb, aab=ba〉 Finite non-commutative monoid with 13 elements
10 〈a, b | aaa=b, abbbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
10 〈a, b | aab=b, abbba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
10 〈a, b | bb=aa, aaab=ba〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=aa, bbbb=a〉 Finite commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aaab=ab, bbbb=a〉 Finite commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaab=bb, bbbb=a〉 Finite commutative monoid with 13 elements 14 isomorphic
11 〈a, b | aaab=b, aabba=a〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | aaa=bb, aabbb=b〉 Finite commutative monoid with 13 elements 2 isomorphic
11 〈a, b | aaa=ab, abbb=bb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, abbb=ba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aaa=bb, babb=ab〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=ab, bbbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbbb=aa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aba=bb, abbb=aa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ab, bbb=aaa〉 Finite non-commutative monoid with 13 elements 1 isomorphic
11 〈a, b | aab=ba, bbb=aaa〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbbbb=a〉 Finite commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=b, ababba=a〉 Finite non-commutative monoid with 13 elements 4 isomorphic
11 〈a, b | aab=a, baaa=bbb〉 Finite non-commutative monoid with 13 elements
11 〈a, b | aab=a, bbbb=bba〉 Finite non-commutative monoid with 13 elements
11 〈a, b | ab=aa, aaaa=bbb〉 Finite non-commutative monoid with 13 elements 7 isomorphic
11 〈a, b | ab=aa, baaa=bbb〉 Finite non-commutative monoid with 13 elements 3 isomorphic
11 〈a, b | ab=a, baaaaaa=b〉 Finite non-commutative monoid with 13 elements

Other isomorphic instances

2 total

Length:Presentation:
11〈a, b | aaba=b, bbabb=a〉
11〈a, b | aaba=b, bbbab=a〉