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〈a, b | aa=1, abb=b〉

Monoid presentation of length 6

Properties

Completion parameters

Complete rewriting system

  1. ab ⇒ b2
  2. a2 ⇒ 1
  3. b3 ⇒ b

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1abbab2b2a
11abbab2b2a
aa1b2b2abba
bbbab2b2abba
bababbbab2b2a
b2b2b2abbab2b2a
b2ab2ab2b2b2abba

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

25 unique, 1895 total

Length:Presentation:Description:Related:
6 〈a, b | ab=aa, bb=1〉 Finite non-commutative monoid with 6 elements 22 isomorphic
6 〈a, b | aaa=1, abb=1〉 Isomorphic to ℤ6 1373 isomorphic
7 〈a, b | ab=aa, bb=b〉 Finite non-commutative monoid with 6 elements
7 〈a, b | aa=a, bbb=a〉 Finite commutative monoid with 6 elements 49 isomorphic
7 〈a, b | aa=b, bbb=a〉 Finite commutative monoid with 6 elements 61 isomorphic
7 〈a, b | aa=b, bbb=b〉 Finite commutative monoid with 6 elements 55 isomorphic
7 〈a, b | aa=1, abab=b〉 Finite non-commutative monoid with 6 elements 31 isomorphic, 22 anti-isomorphic
8 〈a, b | ab=aa, baa=b〉 Finite non-commutative monoid with 6 elements 4 isomorphic
8 〈a, b | ab=aa, bbb=a〉 Finite commutative monoid with 6 elements 46 isomorphic
8 〈a, b | aa=a, abbb=b〉 Finite non-commutative monoid with 6 elements 19 isomorphic
8 〈a, b | aa=a, aab=bb〉 Finite non-commutative monoid with 6 elements 3 isomorphic
8 〈a, b | ab=a, baa=bb〉 Finite non-commutative monoid with 6 elements 12 isomorphic, 1 anti-isomorphic
9 〈a, b | abba=b, baba=1〉 Finite non-Abelian group with 6 elements 66 isomorphic
9 〈a, b | aaa=aa, abb=b〉 Finite non-commutative monoid with 6 elements 5 isomorphic
9 〈a, b | aab=bb, abb=a〉 Finite commutative monoid with 6 elements 13 isomorphic
9 〈a, b | aba=aa, baa=b〉 Finite non-commutative monoid with 6 elements
9 〈a, b | abb=aa, bbb=a〉 Finite commutative monoid with 6 elements 49 isomorphic
9 〈a, b | ab=a, aaaa=bb〉 Finite commutative monoid with 6 elements 14 isomorphic
9 〈a, b | ab=a, bbbb=aa〉 Finite commutative monoid with 6 elements 5 isomorphic
9 〈a, b | ab=a, bbbb=ba〉 Finite non-commutative monoid with 6 elements 2 isomorphic
9 〈a, b | ab=a, bbb=aaa〉 Finite commutative monoid with 6 elements 9 isomorphic
9 〈a, b | ab=a, bbb=bba〉 Finite non-commutative monoid with 6 elements 3 isomorphic
10 〈a, b | aba=aa, aabb=b〉 Finite non-commutative monoid with 6 elements 5 isomorphic
10 〈a, b | aab=b, aaba=aa〉 Finite non-commutative monoid with 6 elements 1 isomorphic
11 〈a, b | aa=a, abbbbba=b〉 Finite commutative monoid with 6 elements

Other isomorphic instances

30 total

Length:Presentation:
8〈a, b | aa=1, aaabb=b〉
8〈a, b | aa=1, abaab=b〉
8〈a, b | aa=1, aaab=bb〉
8〈a, b | aa=1, aabb=ab〉
8〈a, b | aa=1, baab=ab〉
8〈a, b | aa=1, abb=aab〉
8〈a, b | aa=1, baa=abb〉
10〈a, b | aa=1, aaaaabb=b〉
10〈a, b | aa=1, aaabaab=b〉
10〈a, b | aa=1, aaabbaa=b〉
10〈a, b | aa=1, abaaaab=b〉
10〈a, b | aa=1, aaaaab=bb〉
10〈a, b | aa=1, aaaabb=ab〉
10〈a, b | aa=1, aaabaa=bb〉
10〈a, b | aa=1, aaabba=ba〉
10〈a, b | aa=1, aabaab=ab〉
10〈a, b | aa=1, aabbaa=ab〉
10〈a, b | aa=1, baaaab=ab〉
10〈a, b | aa=1, aaaab=abb〉
10〈a, b | aa=1, aaaba=bba〉
10〈a, b | aa=1, aaabb=aab〉
10〈a, b | aa=1, aaabb=baa〉
10〈a, b | aa=1, aabaa=abb〉
10〈a, b | aa=1, aabba=aba〉
10〈a, b | aa=1, abaab=aab〉
10〈a, b | aa=1, abaab=baa〉
10〈a, b | aa=1, aabb=aaab〉
10〈a, b | aa=1, abaa=aabb〉
10〈a, b | aa=1, abba=aaba〉
10〈a, b | aa=1, baab=aaab〉