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〈a, b | ab=aa, baaaaa=b〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. ba ⇒ b2
  2. a2 ⇒ ab
  3. b6 ⇒ b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1ababb2ab2b3ab3b4ab4b5ab5
11ababb2ab2b3ab3b4ab4b5ab5
aaababab2ab2ab3ab3ab4ab4ab5ab5ab
bbb2b2b3b3b4b4b5b5bbb2
ababab2ab2ab3ab3ab4ab4ab5ab5ababab2
b2b2b3b3b4b4b5b5bbb2b2b3
ab2ab2ab3ab3ab4ab4ab5ab5ababab2ab2ab3
b3b3b4b4b5b5bbb2b2b3b3b4
ab3ab3ab4ab4ab5ab5ababab2ab2ab3ab3ab4
b4b4b5b5bbb2b2b3b3b4b4b5
ab4ab4ab5ab5ababab2ab2ab3ab3ab4ab4ab5
b5b5bbb2b2b3b3b4b4b5b5b
ab5ab5ababab2ab2ab3ab3ab4ab4ab5ab5ab

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

51 unique, 629 total

Length:Presentation:Description:Related:
7 〈a, b | aab=a, bbb=1〉 Finite non-commutative monoid with 12 elements 8 isomorphic, 12 anti-isomorphic
7 〈a, b | ab=aa, bbb=1〉 Finite non-commutative monoid with 12 elements 9 isomorphic
8 〈a, b | aba=ab, bbb=1〉 Finite non-commutative monoid with 12 elements
8 〈a, b | aaaa=1, abbb=1〉 Isomorphic to ℤ12 325 isomorphic
8 〈a, b | ab=aa, bbb=b〉 Finite non-commutative monoid with 12 elements
8 〈a, b | aaa=1, aabb=b〉 Finite non-commutative monoid with 12 elements 16 isomorphic
9 〈a, b | aab=bb, aba=a〉 Finite non-commutative monoid with 12 elements 2 isomorphic
9 〈a, b | aba=b, aaabb=1〉 Finite non-Abelian group with 12 elements 19 isomorphic
9 〈a, b | aaa=a, bbbb=a〉 Finite commutative monoid with 12 elements 6 isomorphic
9 〈a, b | aaa=b, bbbb=a〉 Finite commutative monoid with 12 elements 27 isomorphic
9 〈a, b | aaa=b, bbbb=b〉 Finite commutative monoid with 12 elements 23 isomorphic
9 〈a, b | ab=aa, bbb=bb〉 Finite non-commutative monoid with 12 elements
9 〈a, b | aaa=1, aabab=b〉 Finite non-commutative monoid with 12 elements 8 isomorphic, 4 anti-isomorphic
10 〈a, b | bab=aba, aabb=1〉 Finite non-Abelian group with 12 elements 4 isomorphic
10 〈a, b | aaa=aa, bbbb=a〉 Finite commutative monoid with 12 elements
10 〈a, b | aaa=ab, bbbb=a〉 Finite commutative monoid with 12 elements 7 isomorphic
10 〈a, b | aaa=bb, bbbb=a〉 Finite commutative monoid with 12 elements 43 isomorphic
10 〈a, b | aab=bb, abba=a〉 Finite non-commutative monoid with 12 elements 6 isomorphic
10 〈a, b | aaa=ab, bab=bb〉 Finite non-commutative monoid with 12 elements 1 isomorphic
10 〈a, b | aaa=a, aaab=bb〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aaa=b, bbbb=bb〉 Finite commutative monoid with 12 elements 4 isomorphic
10 〈a, b | aab=a, bbbb=ba〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aab=a, bbbb=bb〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aba=a, bbbb=ab〉 Finite non-commutative monoid with 12 elements
10 〈a, b | ab=aa, bbaa=bb〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaaa=aa, abab=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aaab=bb, aaba=a〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=aaa, baaa=b〉 Finite non-commutative monoid with 12 elements 4 isomorphic
11 〈a, b | aab=aaa, bbbb=a〉 Finite commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=ba, ababbb=1〉 Finite non-Abelian group with 12 elements 5 isomorphic
11 〈a, b | aaa=aa, abbbb=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aaa=ab, aabb=bb〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaa=bb, aabb=ab〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaa=bb, aabb=ba〉 Finite non-commutative monoid with 12 elements 1 isomorphic
11 〈a, b | aab=aa, abab=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aab=bb, aaaa=ab〉 Finite non-commutative monoid with 12 elements 1 isomorphic
11 〈a, b | aab=bb, aaaa=ba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aba=bb, aabb=aa〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=a, baaaa=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aba=b, bbbbb=aa〉 Finite commutative monoid with 12 elements
11 〈a, b | aaa=b, bbbb=abb〉 Finite commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=a, bbaa=bbb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aab=b, aaaa=bba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | bb=aa, aaaaab=a〉 Finite commutative monoid with 12 elements 15 isomorphic
11 〈a, b | ab=aa, baaaa=bb〉 Finite non-commutative monoid with 12 elements 7 isomorphic
11 〈a, b | bb=aa, aaaa=aba〉 Finite non-commutative monoid with 12 elements 4 isomorphic
11 〈a, b | bb=aa, aaab=aba〉 Finite non-commutative monoid with 12 elements 3 isomorphic
11 〈a, b | bb=aa, abab=aba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aa=a, abbbbbb=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=a, baaaaa=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=a, bbaaa=bbb〉 Finite non-commutative monoid with 12 elements

Other isomorphic instances

30 total

Length:Presentation:
11〈a, b | ab=aa, baaaab=b〉
11〈a, b | ab=aa, baaaba=b〉
11〈a, b | ab=aa, baaabb=b〉
11〈a, b | ab=aa, baabaa=b〉
11〈a, b | ab=aa, baabab=b〉
11〈a, b | ab=aa, baabba=b〉
11〈a, b | ab=aa, baabbb=b〉
11〈a, b | ab=aa, babaaa=b〉
11〈a, b | ab=aa, babaab=b〉
11〈a, b | ab=aa, bababa=b〉
11〈a, b | ab=aa, bababb=b〉
11〈a, b | ab=aa, babbaa=b〉
11〈a, b | ab=aa, babbab=b〉
11〈a, b | ab=aa, babbba=b〉
11〈a, b | ab=aa, babbbb=b〉
11〈a, b | ab=aa, bbaaaa=b〉
11〈a, b | ab=aa, bbaaab=b〉
11〈a, b | ab=aa, bbaaba=b〉
11〈a, b | ab=aa, bbaabb=b〉
11〈a, b | ab=aa, bbabaa=b〉
11〈a, b | ab=aa, bbabab=b〉
11〈a, b | ab=aa, bbabba=b〉
11〈a, b | ab=aa, bbabbb=b〉
11〈a, b | ab=aa, bbbaaa=b〉
11〈a, b | ab=aa, bbbaab=b〉
11〈a, b | ab=aa, bbbaba=b〉
11〈a, b | ab=aa, bbbabb=b〉
11〈a, b | ab=aa, bbbbaa=b〉
11〈a, b | ab=aa, bbbbab=b〉
11〈a, b | ab=aa, bbbbba=b〉