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〈a, b | aa=1, abbb=b〉

Monoid presentation of length 7

Properties

Completion parameters

Complete rewriting system

  1. b5 ⇒ b
  2. ab ⇒ b3
  3. a2 ⇒ 1

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1abbab2b2ab3b3ab4b4a
11abbab2b2ab3b3ab4b4a
aa1b3b3ab4b4abbab2b2a
bbbab2b2ab3b3ab4b4abba
bababb4b4abbab2b2ab3b3a
b2b2b2ab3b3ab4b4abbab2b2a
b2ab2ab2bbab2b2ab3b3ab4b4a
b3b3b3ab4b4abbab2b2ab3b3a
b3ab3ab3b2b2ab3b3ab4b4abba
b4b4b4abbab2b2ab3b3ab4b4a
b4ab4ab4b3b3ab4b4abbab2b2a

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

37 unique, 834 total

Length:Presentation:Description:Related:
8 〈a, b | aaa=b, abbb=1〉 Isomorphic to ℤ10 536 isomorphic
8 〈a, b | bb=aa, aba=a〉 Finite non-commutative monoid with 10 elements 1 isomorphic
8 〈a, b | bb=aa, aba=b〉 Finite non-commutative monoid with 10 elements 1 isomorphic
8 〈a, b | aa=a, bbb=ab〉 Finite non-commutative monoid with 10 elements 3 isomorphic
9 〈a, b | aab=bb, bba=a〉 Finite non-commutative monoid with 10 elements 6 isomorphic
9 〈a, b | aaa=b, abbb=a〉 Finite commutative monoid with 10 elements 59 isomorphic
9 〈a, b | aaa=b, abbb=b〉 Finite commutative monoid with 10 elements 35 isomorphic
9 〈a, b | bb=aa, aba=aa〉 Finite non-commutative monoid with 10 elements 1 isomorphic
9 〈a, b | aa=a, bbbbb=a〉 Finite commutative monoid with 10 elements 17 isomorphic
9 〈a, b | aa=b, bbbbb=b〉 Finite commutative monoid with 10 elements 57 isomorphic
10 〈a, b | aaaa=b, aabb=b〉 Finite commutative monoid with 10 elements 20 isomorphic
10 〈a, b | aaa=bb, abb=ab〉 Finite non-commutative monoid with 10 elements 2 isomorphic
10 〈a, b | aaa=bb, abb=ba〉 Finite non-commutative monoid with 10 elements
10 〈a, b | aab=aa, aba=bb〉 Finite non-commutative monoid with 10 elements
10 〈a, b | aaa=b, abbb=bb〉 Finite commutative monoid with 10 elements 3 isomorphic
10 〈a, b | aab=a, baaa=bb〉 Finite non-commutative monoid with 10 elements
10 〈a, b | ab=aa, baaaa=b〉 Finite non-commutative monoid with 10 elements 14 isomorphic
10 〈a, b | ab=aa, baaa=bb〉 Finite non-commutative monoid with 10 elements 3 isomorphic
10 〈a, b | aa=a, abbbbb=b〉 Finite non-commutative monoid with 10 elements 5 isomorphic
10 〈a, b | ab=a, baaaa=bb〉 Finite non-commutative monoid with 10 elements 4 isomorphic
11 〈a, b | aaab=baa, abab=1〉 Finite non-Abelian group with 10 elements 3 isomorphic
11 〈a, b | aaaa=aa, abba=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aaaa=ab, baaa=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aaaa=bb, aaab=a〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aaaa=bb, aaab=b〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aabb=aa, bbbb=a〉 Finite commutative monoid with 10 elements 3 isomorphic
11 〈a, b | abab=aa, baab=b〉 Finite non-commutative monoid with 10 elements 4 isomorphic
11 〈a, b | aab=bb, aaaaa=b〉 Finite commutative monoid with 10 elements 7 isomorphic
11 〈a, b | aab=bb, abbbb=a〉 Finite commutative monoid with 10 elements 5 isomorphic
11 〈a, b | aba=aa, aaaab=b〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aab=b, abbbb=aa〉 Finite commutative monoid with 10 elements 5 isomorphic
11 〈a, b | aaa=b, abbb=bbb〉 Finite commutative monoid with 10 elements 1 isomorphic
11 〈a, b | aab=a, bbbb=bab〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aab=b, aaaa=baa〉 Finite non-commutative monoid with 10 elements
11 〈a, b | aba=b, aaaa=bbb〉 Finite commutative monoid with 10 elements
11 〈a, b | ab=a, bbbb=baaa〉 Finite non-commutative monoid with 10 elements
11 〈a, b | ab=a, bbbb=bbaa〉 Finite non-commutative monoid with 10 elements

Other isomorphic instances

51 total

Length:Presentation:
7〈a, b | aa=1, bbb=ab〉
9〈a, b | aa=1, aaabbb=b〉
9〈a, b | aa=1, abaabb=b〉
9〈a, b | aa=1, ababab=b〉
9〈a, b | aa=1, abbaab=b〉
9〈a, b | aa=1, aabbb=ab〉
9〈a, b | aa=1, baabb=ab〉
9〈a, b | aa=1, babab=ab〉
9〈a, b | aa=1, aaab=bbb〉
9〈a, b | aa=1, abbb=aab〉
9〈a, b | aa=1, abbb=baa〉
11〈a, b | aa=1, aaaaabbb=b〉
11〈a, b | aa=1, aaabaabb=b〉
11〈a, b | aa=1, aaababab=b〉
11〈a, b | aa=1, aaabbaab=b〉
11〈a, b | aa=1, aaabbbaa=b〉
11〈a, b | aa=1, abaaaabb=b〉
11〈a, b | aa=1, abaaabab=b〉
11〈a, b | aa=1, abaabaab=b〉
11〈a, b | aa=1, ababaaab=b〉
11〈a, b | aa=1, abbaaaab=b〉
11〈a, b | aa=1, aaaabbb=ab〉
11〈a, b | aa=1, aaabbba=ba〉
11〈a, b | aa=1, aabaabb=ab〉
11〈a, b | aa=1, aababab=ab〉
11〈a, b | aa=1, aabbaab=ab〉
11〈a, b | aa=1, aabbbaa=ab〉
11〈a, b | aa=1, abaabba=ba〉
11〈a, b | aa=1, baaaabb=ab〉
11〈a, b | aa=1, baaabab=ab〉
11〈a, b | aa=1, baabaab=ab〉
11〈a, b | aa=1, aaaaab=bbb〉
11〈a, b | aa=1, aaabaa=bbb〉
11〈a, b | aa=1, aaabbb=aab〉
11〈a, b | aa=1, aaabbb=baa〉
11〈a, b | aa=1, aabbba=aba〉
11〈a, b | aa=1, abaabb=aab〉
11〈a, b | aa=1, abaabb=baa〉
11〈a, b | aa=1, ababab=aab〉
11〈a, b | aa=1, ababab=baa〉
11〈a, b | aa=1, abbaab=aab〉
11〈a, b | aa=1, abbaab=baa〉
11〈a, b | aa=1, aaaab=abbb〉
11〈a, b | aa=1, aaaba=bbba〉
11〈a, b | aa=1, aabaa=abbb〉
11〈a, b | aa=1, aabbb=aaab〉
11〈a, b | aa=1, aabbb=abaa〉
11〈a, b | aa=1, abbba=aaba〉
11〈a, b | aa=1, baabb=aaab〉
11〈a, b | aa=1, baabb=abaa〉
11〈a, b | aa=1, babab=aaab〉

Other anti-isomorphic instances

34 total

Length:Presentation:
9〈a, b | aa=1, aabbba=b〉
9〈a, b | aa=1, aabbb=ba〉
9〈a, b | aa=1, abbba=ab〉
9〈a, b | aa=1, baabb=ba〉
9〈a, b | aa=1, aaba=bbb〉
9〈a, b | aa=1, abbb=aba〉
11〈a, b | aa=1, aaaabbba=b〉
11〈a, b | aa=1, aabaabba=b〉
11〈a, b | aa=1, aabababa=b〉
11〈a, b | aa=1, aabbaaba=b〉
11〈a, b | aa=1, aaaabbb=ba〉
11〈a, b | aa=1, aaabbba=ab〉
11〈a, b | aa=1, aabaabb=ba〉
11〈a, b | aa=1, aababab=ba〉
11〈a, b | aa=1, aabbaab=ba〉
11〈a, b | aa=1, abaabba=ab〉
11〈a, b | aa=1, abababa=ab〉
11〈a, b | aa=1, baaaabb=ba〉
11〈a, b | aa=1, baaabab=ba〉
11〈a, b | aa=1, aaaaba=bbb〉
11〈a, b | aa=1, aaabbb=aba〉
11〈a, b | aa=1, aabbba=aab〉
11〈a, b | aa=1, aabbba=baa〉
11〈a, b | aa=1, abaabb=aba〉
11〈a, b | aa=1, ababab=aba〉
11〈a, b | aa=1, abbaab=aba〉
11〈a, b | aa=1, aaaab=bbba〉
11〈a, b | aa=1, aaaba=abbb〉
11〈a, b | aa=1, aabbb=aaba〉
11〈a, b | aa=1, aabbb=baaa〉
11〈a, b | aa=1, abbba=aaab〉
11〈a, b | aa=1, baabb=aaba〉
11〈a, b | aa=1, baabb=baaa〉
11〈a, b | aa=1, babab=aaba〉