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〈a, b | aaa=bb, abb=b〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. a8 ⇒ a3
  2. b ⇒ a4

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aa2a3a4a5a6a7
11aa2a3a4a5a6a7
aaa2a3a4a5a6a7a3
a2a2a3a4a5a6a7a3a4
a3a3a4a5a6a7a3a4a5
a4a4a5a6a7a3a4a5a6
a5a5a6a7a3a4a5a6a7
a6a6a7a3a4a5a6a7a3
a7a7a3a4a5a6a7a3a4

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

44 unique, 1156 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, 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 | aab=bb, abbb=a〉 Finite commutative monoid with 8 elements 10 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

55 total

Length:Presentation:
9〈a, b | aaa=b, aabb=b〉
9〈a, b | aaa=b, abab=b〉
9〈a, b | aaa=b, abba=b〉
9〈a, b | aaa=b, baab=b〉
9〈a, b | aa=b, bbbb=ab〉
10〈a, b | aaa=ab, abbb=b〉
10〈a, b | aaa=bb, aaaa=b〉
10〈a, b | aa=b, aabbb=ab〉
10〈a, b | aa=b, aabbb=ba〉
10〈a, b | aa=b, ababb=ab〉
10〈a, b | aa=b, ababb=ba〉
10〈a, b | aa=b, abbab=ab〉
10〈a, b | aa=b, abbab=ba〉
10〈a, b | aa=b, abbba=ab〉
10〈a, b | aa=b, baabb=ab〉
10〈a, b | aa=b, baabb=ba〉
10〈a, b | aa=b, babab=ab〉
10〈a, b | aa=b, bbbb=aaa〉
11〈a, b | aaa=ab, aaabb=b〉
11〈a, b | aaa=ab, aabab=b〉
11〈a, b | aaa=ab, aabba=b〉
11〈a, b | aaa=ab, abaab=b〉
11〈a, b | aaa=ab, ababa=b〉
11〈a, b | aaa=ab, abbaa=b〉
11〈a, b | aaa=b, aaaaab=b〉
11〈a, b | aaa=b, aaaaba=b〉
11〈a, b | aaa=b, aaabaa=b〉
11〈a, b | aaa=b, aabb=aaa〉
11〈a, b | aaa=b, abab=aaa〉
11〈a, b | aaa=b, abba=aaa〉
11〈a, b | aaa=b, baab=aaa〉
11〈a, b | aab=a, aaab=bbb〉
11〈a, b | aab=a, aaba=bbb〉
11〈a, b | aab=a, abaa=bbb〉
11〈a, b | aa=b, aaaabb=ab〉
11〈a, b | aa=b, aaaabb=ba〉
11〈a, b | aa=b, aaabab=ab〉
11〈a, b | aa=b, aaabab=ba〉
11〈a, b | aa=b, aaabba=ab〉
11〈a, b | aa=b, aaabba=ba〉
11〈a, b | aa=b, aabaab=ab〉
11〈a, b | aa=b, aabaab=ba〉
11〈a, b | aa=b, aababa=ab〉
11〈a, b | aa=b, aababa=ba〉
11〈a, b | aa=b, aabbaa=ab〉
11〈a, b | aa=b, abaaab=ab〉
11〈a, b | aa=b, abaaab=ba〉
11〈a, b | aa=b, abaaba=ab〉
11〈a, b | aa=b, baaaab=ab〉
11〈a, b | aa=b, aabbb=aaa〉
11〈a, b | aa=b, ababb=aaa〉
11〈a, b | aa=b, abbab=aaa〉
11〈a, b | aa=b, abbba=aaa〉
11〈a, b | aa=b, baabb=aaa〉
11〈a, b | aa=b, babab=aaa〉