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〈a, b | aab=bb, abbb=a〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a7 ⇒ a
  2. ba ⇒ a3
  3. ab ⇒ a3
  4. b2 ⇒ a4

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2a3a4a5a6
11aba2a3a4a5a6
aaa2a3a3a4a5a6a
bba3a4a4a5a6aa2
a2a2a3a4a4a5a6aa2
a3a3a4a5a5a6aa2a3
a4a4a5a6a6aa2a3a4
a5a5a6aaa2a3a4a5
a6a6aa2a2a3a4a5a6

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

44 unique, 1201 total

Length:Presentation:Description:Related:
7 〈a, b | aab=1, bbbb=1〉 Isomorphic to ℤ8 727 isomorphic
7 〈a, b | aa=1, abba=b〉 Finite non-commutative monoid with 8 elements 46 isomorphic
8 〈a, b | aba=b, aabb=1〉 Finite non-Abelian group with 8 elements 28 isomorphic
8 〈a, b | aa=a, bbbb=a〉 Finite commutative monoid with 8 elements 48 isomorphic
8 〈a, b | aa=b, bbbb=a〉 Finite commutative monoid with 8 elements 34 isomorphic
8 〈a, b | aa=b, bbbb=b〉 Finite commutative monoid with 8 elements 46 isomorphic
8 〈a, b | aa=a, aba=bb〉 Finite non-commutative monoid with 8 elements 5 isomorphic
8 〈a, b | aa=1, ababa=b〉 Finite non-commutative monoid with 8 elements 13 isomorphic
9 〈a, b | aaa=bb, abb=b〉 Finite commutative monoid with 8 elements 55 isomorphic
9 〈a, b | aaa=bb, bab=a〉 Finite commutative monoid with 8 elements 9 isomorphic
9 〈a, b | aab=aa, baa=b〉 Finite non-commutative monoid with 8 elements 8 isomorphic
9 〈a, b | aab=bb, baa=a〉 Finite non-commutative monoid with 8 elements 4 anti-isomorphic
9 〈a, b | ab=aa, baaa=b〉 Finite non-commutative monoid with 8 elements 6 isomorphic
9 〈a, b | ab=aa, bbbb=a〉 Finite commutative monoid with 8 elements 32 isomorphic
9 〈a, b | bb=aa, aaab=a〉 Finite commutative monoid with 8 elements 3 isomorphic
9 〈a, b | ab=aa, baa=bb〉 Finite non-commutative monoid with 8 elements 1 isomorphic
9 〈a, b | ab=aa, bbb=aa〉 Finite non-commutative monoid with 8 elements 1 isomorphic
9 〈a, b | ab=aa, bbb=ba〉 Finite non-commutative monoid with 8 elements
9 〈a, b | aa=a, abbbb=b〉 Finite non-commutative monoid with 8 elements 14 isomorphic
9 〈a, b | ab=a, baaa=bb〉 Finite non-commutative monoid with 8 elements 9 isomorphic
9 〈a, b | ab=a, bbaa=bb〉 Finite non-commutative monoid with 8 elements 9 isomorphic
10 〈a, b | aab=bb, aaaa=b〉 Finite commutative monoid with 8 elements 18 isomorphic
10 〈a, b | aba=aa, aaab=b〉 Finite non-commutative monoid with 8 elements 3 isomorphic
10 〈a, b | aab=a, bbaa=bb〉 Finite non-commutative monoid with 8 elements
10 〈a, b | aab=b, aaaa=ba〉 Finite non-commutative monoid with 8 elements
10 〈a, b | aab=b, abaa=aa〉 Finite non-commutative monoid with 8 elements 1 isomorphic
10 〈a, b | aab=b, abbb=aa〉 Finite commutative monoid with 8 elements 4 isomorphic
10 〈a, b | ab=aa, aaaa=bb〉 Finite non-commutative monoid with 8 elements 7 isomorphic
10 〈a, b | ab=a, bbbb=baa〉 Finite non-commutative monoid with 8 elements 2 isomorphic
11 〈a, b | aabb=aa, abaa=b〉 Finite commutative monoid with 8 elements 7 isomorphic
11 〈a, b | aabb=aa, bbba=b〉 Finite non-commutative monoid with 8 elements
11 〈a, b | abbb=aa, bbbb=a〉 Finite commutative monoid with 8 elements 14 isomorphic
11 〈a, b | aab=b, aabaa=aa〉 Finite non-commutative monoid with 8 elements 2 isomorphic
11 〈a, b | aab=a, bbbb=bbb〉 Finite non-commutative monoid with 8 elements
11 〈a, b | aab=b, aaaa=aba〉 Finite non-commutative monoid with 8 elements
11 〈a, b | aab=b, aaaa=abb〉 Finite commutative monoid with 8 elements 1 isomorphic
11 〈a, b | ab=a, aaaaaa=bb〉 Finite commutative monoid with 8 elements
11 〈a, b | ab=a, bbbbbb=aa〉 Finite commutative monoid with 8 elements
11 〈a, b | ab=a, bbbbbb=ba〉 Finite non-commutative monoid with 8 elements
11 〈a, b | ab=a, aaaaa=bbb〉 Finite commutative monoid with 8 elements
11 〈a, b | ab=a, bbbbb=aaa〉 Finite commutative monoid with 8 elements
11 〈a, b | ab=a, bbbbb=bba〉 Finite non-commutative monoid with 8 elements
11 〈a, b | ab=a, bbbb=aaaa〉 Finite commutative monoid with 8 elements
11 〈a, b | ab=a, bbbb=bbba〉 Finite non-commutative monoid with 8 elements

Other isomorphic instances

10 total

Length:Presentation:
10〈a, b | aab=bb, babb=a〉
10〈a, b | aab=bb, bbab=a〉
10〈a, b | aba=bb, babb=a〉
11〈a, b | aab=bb, aaabb=a〉
11〈a, b | aab=bb, aabab=a〉
11〈a, b | aab=bb, abaab=a〉
11〈a, b | aab=bb, baaab=a〉
11〈a, b | aba=bb, aaabb=a〉
11〈a, b | aba=bb, aabba=a〉
11〈a, b | aba=bb, abaab=a〉