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〈a, b | aa=b, abb=a〉

Monoid presentation of length 7

Properties

Completion parameters

Complete rewriting system

  1. a5 ⇒ a
  2. b ⇒ a2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aa2a3a4
11aa2a3a4
aaa2a3a4a
a2a2a3a4aa2
a3a3a4aa2a3
a4a4aa2a3a4

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

16 unique, 1391 total

Length:Presentation:Description:Related:
6 〈a, b | aa=b, abb=1〉 Isomorphic to ℤ5 1132 isomorphic
7 〈a, b | aa=b, abb=b〉 Finite commutative monoid with 5 elements 43 isomorphic
7 〈a, b | ab=a, baa=b〉 Finite non-commutative monoid with 5 elements 43 isomorphic
8 〈a, b | aaa=b, aab=b〉 Finite commutative monoid with 5 elements 27 isomorphic
8 〈a, b | aab=a, baa=b〉 Finite non-commutative monoid with 5 elements 8 isomorphic
8 〈a, b | aab=b, aba=a〉 Finite non-commutative monoid with 5 elements 8 isomorphic
8 〈a, b | ab=a, bbbb=a〉 Finite commutative monoid with 5 elements 32 isomorphic
8 〈a, b | ab=a, aaa=bb〉 Finite commutative monoid with 5 elements 19 isomorphic
8 〈a, b | ab=a, bba=bb〉 Finite non-commutative monoid with 5 elements 15 isomorphic
8 〈a, b | ab=a, bbb=aa〉 Finite commutative monoid with 5 elements 9 isomorphic
8 〈a, b | ab=a, bbb=ba〉 Finite non-commutative monoid with 5 elements 4 isomorphic
9 〈a, b | aab=aa, bba=b〉 Finite non-commutative monoid with 5 elements 9 isomorphic
9 〈a, b | aab=b, aaba=a〉 Finite non-commutative monoid with 5 elements 10 isomorphic
10 〈a, b | aa=a, abbbba=b〉 Finite commutative monoid with 5 elements 3 isomorphic
11 〈a, b | aabb=a, baabb=b〉 Finite non-commutative monoid with 5 elements 10 isomorphic, 3 anti-isomorphic
11 〈a, b | aaa=aa, abbba=b〉 Finite commutative monoid with 5 elements

Other isomorphic instances

71 total

Length:Presentation:
7〈a, b | aa=b, bab=a〉
8〈a, b | aaa=b, aab=a〉
8〈a, b | aaa=b, aba=a〉
8〈a, b | aa=b, aaab=a〉
8〈a, b | aa=b, aaba=a〉
8〈a, b | ab=a, aaaa=b〉
9〈a, b | aab=b, aabb=a〉
9〈a, b | aab=b, abab=a〉
9〈a, b | aab=b, baab=a〉
9〈a, b | aba=b, aabb=a〉
9〈a, b | aba=b, abab=a〉
9〈a, b | aba=b, abba=a〉
9〈a, b | aa=b, aaaaa=a〉
9〈a, b | ab=a, aaaab=b〉
9〈a, b | ab=a, aaaba=b〉
9〈a, b | ab=a, aabaa=b〉
9〈a, b | ab=a, abaaa=b〉
10〈a, b | aaa=b, aaaaa=a〉
10〈a, b | aab=a, aaaab=b〉
10〈a, b | aab=a, aaaba=b〉
10〈a, b | aab=a, aabaa=b〉
10〈a, b | aab=a, abaaa=b〉
10〈a, b | aba=a, aaaba=b〉
10〈a, b | aba=a, aabaa=b〉
10〈a, b | ab=a, aaaabb=b〉
10〈a, b | ab=a, aaabab=b〉
10〈a, b | ab=a, aaabba=b〉
10〈a, b | ab=a, aabaab=b〉
10〈a, b | ab=a, aababa=b〉
10〈a, b | ab=a, aabbaa=b〉
10〈a, b | ab=a, abaaab=b〉
10〈a, b | ab=a, abaaba=b〉
10〈a, b | ab=a, ababaa=b〉
10〈a, b | ab=a, abbaaa=b〉
11〈a, b | aaaa=b, aaaaa=a〉
11〈a, b | aaab=a, aaaab=b〉
11〈a, b | aaab=a, aaaba=b〉
11〈a, b | aaab=a, aabaa=b〉
11〈a, b | aaab=a, abaaa=b〉
11〈a, b | aaba=a, aaaba=b〉
11〈a, b | aaba=a, aabaa=b〉
11〈a, b | aaba=a, abaaa=b〉
11〈a, b | aab=b, aaaabb=a〉
11〈a, b | aab=b, aaabab=a〉
11〈a, b | aab=b, aabaab=a〉
11〈a, b | aab=b, abaaab=a〉
11〈a, b | aab=b, baaaab=a〉
11〈a, b | aba=b, aaabab=a〉
11〈a, b | aba=b, aabaab=a〉
11〈a, b | aba=b, aababa=a〉
11〈a, b | aba=b, abaaba=a〉
11〈a, b | ab=a, aaaabbb=b〉
11〈a, b | ab=a, aaababb=b〉
11〈a, b | ab=a, aaabbab=b〉
11〈a, b | ab=a, aaabbba=b〉
11〈a, b | ab=a, aabaabb=b〉
11〈a, b | ab=a, aababab=b〉
11〈a, b | ab=a, aababba=b〉
11〈a, b | ab=a, aabbaab=b〉
11〈a, b | ab=a, aabbaba=b〉
11〈a, b | ab=a, aabbbaa=b〉
11〈a, b | ab=a, abaaabb=b〉
11〈a, b | ab=a, abaabab=b〉
11〈a, b | ab=a, abaabba=b〉
11〈a, b | ab=a, ababaab=b〉
11〈a, b | ab=a, abababa=b〉
11〈a, b | ab=a, ababbaa=b〉
11〈a, b | ab=a, abbaaab=b〉
11〈a, b | ab=a, abbaaba=b〉
11〈a, b | ab=a, abbabaa=b〉
11〈a, b | ab=a, abbbaaa=b〉