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〈a, b | aaa=b, bbbb=a〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. a12 ⇒ a
  2. b ⇒ a3

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aa2a3a4a5a6a7a8a9a10a11
11aa2a3a4a5a6a7a8a9a10a11
aaa2a3a4a5a6a7a8a9a10a11a
a2a2a3a4a5a6a7a8a9a10a11aa2
a3a3a4a5a6a7a8a9a10a11aa2a3
a4a4a5a6a7a8a9a10a11aa2a3a4
a5a5a6a7a8a9a10a11aa2a3a4a5
a6a6a7a8a9a10a11aa2a3a4a5a6
a7a7a8a9a10a11aa2a3a4a5a6a7
a8a8a9a10a11aa2a3a4a5a6a7a8
a9a9a10a11aa2a3a4a5a6a7a8a9
a10a10a11aa2a3a4a5a6a7a8a9a10
a11a11aa2a3a4a5a6a7a8a9a10a11

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

51 unique, 632 total

Length:Presentation:Description:Related:
7 〈a, b | aab=a, bbb=1〉 Finite non-commutative monoid with 12 elements 8 isomorphic, 12 anti-isomorphic
7 〈a, b | ab=aa, bbb=1〉 Finite non-commutative monoid with 12 elements 9 isomorphic
8 〈a, b | aba=ab, bbb=1〉 Finite non-commutative monoid with 12 elements
8 〈a, b | aaaa=1, abbb=1〉 Isomorphic to ℤ12 325 isomorphic
8 〈a, b | ab=aa, bbb=b〉 Finite non-commutative monoid with 12 elements
8 〈a, b | aaa=1, aabb=b〉 Finite non-commutative monoid with 12 elements 16 isomorphic
9 〈a, b | aab=bb, aba=a〉 Finite non-commutative monoid with 12 elements 2 isomorphic
9 〈a, b | aba=b, aaabb=1〉 Finite non-Abelian group with 12 elements 19 isomorphic
9 〈a, b | aaa=a, bbbb=a〉 Finite commutative monoid with 12 elements 6 isomorphic
9 〈a, b | aaa=b, bbbb=b〉 Finite commutative monoid with 12 elements 23 isomorphic
9 〈a, b | ab=aa, bbb=bb〉 Finite non-commutative monoid with 12 elements
9 〈a, b | aaa=1, aabab=b〉 Finite non-commutative monoid with 12 elements 8 isomorphic, 4 anti-isomorphic
10 〈a, b | bab=aba, aabb=1〉 Finite non-Abelian group with 12 elements 4 isomorphic
10 〈a, b | aaa=aa, bbbb=a〉 Finite commutative monoid with 12 elements
10 〈a, b | aaa=ab, bbbb=a〉 Finite commutative monoid with 12 elements 7 isomorphic
10 〈a, b | aaa=bb, bbbb=a〉 Finite commutative monoid with 12 elements 43 isomorphic
10 〈a, b | aab=bb, abba=a〉 Finite non-commutative monoid with 12 elements 6 isomorphic
10 〈a, b | aaa=ab, bab=bb〉 Finite non-commutative monoid with 12 elements 1 isomorphic
10 〈a, b | aaa=a, aaab=bb〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aaa=b, bbbb=bb〉 Finite commutative monoid with 12 elements 4 isomorphic
10 〈a, b | aab=a, bbbb=ba〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aab=a, bbbb=bb〉 Finite non-commutative monoid with 12 elements
10 〈a, b | aba=a, bbbb=ab〉 Finite non-commutative monoid with 12 elements
10 〈a, b | ab=aa, bbaa=bb〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaaa=aa, abab=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aaab=bb, aaba=a〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=aaa, baaa=b〉 Finite non-commutative monoid with 12 elements 4 isomorphic
11 〈a, b | aab=aaa, bbbb=a〉 Finite commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=ba, ababbb=1〉 Finite non-Abelian group with 12 elements 5 isomorphic
11 〈a, b | aaa=aa, abbbb=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aaa=ab, aabb=bb〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaa=bb, aabb=ab〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aaa=bb, aabb=ba〉 Finite non-commutative monoid with 12 elements 1 isomorphic
11 〈a, b | aab=aa, abab=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aab=bb, aaaa=ab〉 Finite non-commutative monoid with 12 elements 1 isomorphic
11 〈a, b | aab=bb, aaaa=ba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aba=bb, aabb=aa〉 Finite non-commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=a, baaaa=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aba=b, bbbbb=aa〉 Finite commutative monoid with 12 elements
11 〈a, b | aaa=b, bbbb=abb〉 Finite commutative monoid with 12 elements 2 isomorphic
11 〈a, b | aab=a, bbaa=bbb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aab=b, aaaa=bba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=aa, baaaaa=b〉 Finite non-commutative monoid with 12 elements 30 isomorphic
11 〈a, b | bb=aa, aaaaab=a〉 Finite commutative monoid with 12 elements 15 isomorphic
11 〈a, b | ab=aa, baaaa=bb〉 Finite non-commutative monoid with 12 elements 7 isomorphic
11 〈a, b | bb=aa, aaaa=aba〉 Finite non-commutative monoid with 12 elements 4 isomorphic
11 〈a, b | bb=aa, aaab=aba〉 Finite non-commutative monoid with 12 elements 3 isomorphic
11 〈a, b | bb=aa, abab=aba〉 Finite non-commutative monoid with 12 elements
11 〈a, b | aa=a, abbbbbb=b〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=a, baaaaa=bb〉 Finite non-commutative monoid with 12 elements
11 〈a, b | ab=a, bbaaa=bbb〉 Finite non-commutative monoid with 12 elements

Other isomorphic instances

27 total

Length:Presentation:
10〈a, b | aa=b, bbbbbb=a〉
11〈a, b | aabb=a, aaaaa=b〉
11〈a, b | abab=a, aaaaa=b〉
11〈a, b | abba=a, aaaaa=b〉
11〈a, b | abba=b, bbbbb=a〉
11〈a, b | aaa=b, aaabbb=a〉
11〈a, b | aaa=b, aababb=a〉
11〈a, b | aaa=b, aabbab=a〉
11〈a, b | aaa=b, aabbba=a〉
11〈a, b | aaa=b, abaabb=a〉
11〈a, b | aaa=b, ababab=a〉
11〈a, b | aaa=b, ababba=a〉
11〈a, b | aaa=b, abbaab=a〉
11〈a, b | aaa=b, baaabb=a〉
11〈a, b | aaa=b, baabab=a〉
11〈a, b | aa=b, aabbbbb=a〉
11〈a, b | aa=b, ababbbb=a〉
11〈a, b | aa=b, abbabbb=a〉
11〈a, b | aa=b, abbbabb=a〉
11〈a, b | aa=b, abbbbab=a〉
11〈a, b | aa=b, abbbbba=a〉
11〈a, b | aa=b, baabbbb=a〉
11〈a, b | aa=b, bababbb=a〉
11〈a, b | aa=b, babbabb=a〉
11〈a, b | aa=b, babbbab=a〉
11〈a, b | aa=b, bbaabbb=a〉
11〈a, b | aa=b, bbababb=a〉