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〈a, b | aa=a, bbbb=a〉

Monoid presentation of length 8

Properties

Completion parameters

Complete rewriting system

  1. b8 ⇒ b4
  2. a ⇒ b4

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1bb2b3b4b5b6b7
11bb2b3b4b5b6b7
bbb2b3b4b5b6b7b4
b2b2b3b4b5b6b7b4b5
b3b3b4b5b6b7b4b5b6
b4b4b5b6b7b4b5b6b7
b5b5b6b7b4b5b6b7b4
b6b6b7b4b5b6b7b4b5
b7b7b4b5b6b7b4b5b6

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

44 unique, 1163 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=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, abb=b〉 Finite commutative monoid with 8 elements 55 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

48 total

Length:Presentation:
9〈a, b | aa=a, bbbb=aa〉
9〈a, b | aa=b, bbbb=bb〉
10〈a, b | aaa=b, aabb=ab〉
10〈a, b | aaa=b, aabb=ba〉
10〈a, b | aaa=b, abab=ab〉
10〈a, b | aaa=b, abab=ba〉
10〈a, b | aaa=b, abba=ab〉
10〈a, b | aaa=b, baab=ab〉
10〈a, b | aab=a, bbbb=ab〉
10〈a, b | aa=b, aabbb=bb〉
10〈a, b | aa=b, ababb=bb〉
10〈a, b | aa=b, abbab=bb〉
10〈a, b | aa=b, abbba=bb〉
10〈a, b | aa=b, baabb=bb〉
10〈a, b | aa=b, babab=bb〉
10〈a, b | aa=a, bbbb=aaa〉
10〈a, b | aa=b, bbbb=aab〉
10〈a, b | aa=b, bbbb=aba〉
11〈a, b | aaaa=b, aaaab=b〉
11〈a, b | aaaa=b, aaaba=b〉
11〈a, b | aaaa=b, aabaa=b〉
11〈a, b | aa=b, aaaabb=bb〉
11〈a, b | aa=b, aaabab=bb〉
11〈a, b | aa=b, aaabba=bb〉
11〈a, b | aa=b, aabaab=bb〉
11〈a, b | aa=b, aababa=bb〉
11〈a, b | aa=b, aabbaa=bb〉
11〈a, b | aa=b, abaaab=bb〉
11〈a, b | aa=b, abaaba=bb〉
11〈a, b | aa=b, baaaab=bb〉
11〈a, b | aa=b, aabbb=aab〉
11〈a, b | aa=b, aabbb=aba〉
11〈a, b | aa=b, aabbb=baa〉
11〈a, b | aa=b, ababb=aab〉
11〈a, b | aa=b, ababb=aba〉
11〈a, b | aa=b, ababb=baa〉
11〈a, b | aa=b, abbab=aab〉
11〈a, b | aa=b, abbab=aba〉
11〈a, b | aa=b, abbab=baa〉
11〈a, b | aa=b, abbba=aab〉
11〈a, b | aa=b, abbba=aba〉
11〈a, b | aa=b, baabb=aab〉
11〈a, b | aa=b, baabb=aba〉
11〈a, b | aa=b, baabb=baa〉
11〈a, b | aa=b, babab=aab〉
11〈a, b | aa=b, babab=aba〉
11〈a, b | aa=a, bbbb=aaaa〉
11〈a, b | aa=b, bbbb=aaaa〉