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〈a, b | aaa=b, abbb=a〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. a10 ⇒ a
  2. b ⇒ a3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aa2a3a4a5a6a7a8a9
11aa2a3a4a5a6a7a8a9
aaa2a3a4a5a6a7a8a9a
a2a2a3a4a5a6a7a8a9aa2
a3a3a4a5a6a7a8a9aa2a3
a4a4a5a6a7a8a9aa2a3a4
a5a5a6a7a8a9aa2a3a4a5
a6a6a7a8a9aa2a3a4a5a6
a7a7a8a9aa2a3a4a5a6a7
a8a8a9aa2a3a4a5a6a7a8
a9a9aa2a3a4a5a6a7a8a9

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

37 unique, 860 total

Length:Presentation:Description:Related:
7 〈a, b | aa=1, abbb=b〉 Finite non-commutative monoid with 10 elements 51 isomorphic, 34 anti-isomorphic
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=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

59 total

Length:Presentation:
9〈a, b | aaa=b, babb=a〉
9〈a, b | aa=b, bbbbb=a〉
10〈a, b | aaaa=b, aabb=a〉
10〈a, b | aaaa=b, abab=a〉
10〈a, b | aaaa=b, abba=a〉
10〈a, b | aaaa=b, baab=a〉
10〈a, b | aa=b, aabbbb=a〉
10〈a, b | aa=b, ababbb=a〉
10〈a, b | aa=b, abbabb=a〉
10〈a, b | aa=b, abbbab=a〉
10〈a, b | aa=b, abbbba=a〉
10〈a, b | aa=b, baabbb=a〉
10〈a, b | aa=b, bababb=a〉
10〈a, b | aa=b, babbab=a〉
10〈a, b | aa=b, bbaabb=a〉
11〈a, b | aaab=b, aabbb=a〉
11〈a, b | aaab=b, ababb=a〉
11〈a, b | aaab=b, abbab=a〉
11〈a, b | aaab=b, baabb=a〉
11〈a, b | aaab=b, babab=a〉
11〈a, b | aaab=b, bbaab=a〉
11〈a, b | aaba=b, aabbb=a〉
11〈a, b | aaba=b, ababb=a〉
11〈a, b | aaba=b, abbab=a〉
11〈a, b | aaba=b, abbba=a〉
11〈a, b | aaba=b, baabb=a〉
11〈a, b | aaba=b, babab=a〉
11〈a, b | aaba=b, babba=a〉
11〈a, b | aaba=b, bbaab=a〉
11〈a, b | aaba=b, bbaba=a〉
11〈a, b | aaba=b, bbbaa=a〉
11〈a, b | aaa=b, aaaabb=a〉
11〈a, b | aaa=b, aaabab=a〉
11〈a, b | aaa=b, aaabba=a〉
11〈a, b | aaa=b, aabaab=a〉
11〈a, b | aaa=b, aababa=a〉
11〈a, b | aaa=b, aabbaa=a〉
11〈a, b | aaa=b, abaaab=a〉
11〈a, b | aaa=b, abaaba=a〉
11〈a, b | aaa=b, baaaab=a〉
11〈a, b | aa=b, aaaabbb=a〉
11〈a, b | aa=b, aaababb=a〉
11〈a, b | aa=b, aaabbab=a〉
11〈a, b | aa=b, aaabbba=a〉
11〈a, b | aa=b, aabaabb=a〉
11〈a, b | aa=b, aababab=a〉
11〈a, b | aa=b, aababba=a〉
11〈a, b | aa=b, aabbaab=a〉
11〈a, b | aa=b, aabbaba=a〉
11〈a, b | aa=b, aabbbaa=a〉
11〈a, b | aa=b, abaaabb=a〉
11〈a, b | aa=b, abaabab=a〉
11〈a, b | aa=b, abaabba=a〉
11〈a, b | aa=b, ababaab=a〉
11〈a, b | aa=b, abababa=a〉
11〈a, b | aa=b, abbaaab=a〉
11〈a, b | aa=b, baaaabb=a〉
11〈a, b | aa=b, baaabab=a〉
11〈a, b | aa=b, baabaab=a〉