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〈a, b | aba=a, aaaa=bb〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. b8 ⇒ b2
  2. ab2 ⇒ b7
  3. b2a ⇒ b7
  4. aba ⇒ a
  5. a4 ⇒ b2

Idempotents

4 elements

Cayley table

Idempotents are shown in bold.

1aba2abbab2a3a2bba2babb3a3bba3ba2bb4ba3bb5b6b7
11aba2abbab2a3a2bba2babb3a3bba3ba2bb4ba3bb5b6b7
aaa2aba3a2bab7b2a3ba2abb2b3a3a2bb3a3bb4b5b6
bbbab2ba2babb7b3ba3ba2bb6b2b4ba3bb5b7b5b6b6b7b2
a2a2a3a2bb2a3ba2b6b7b3a3a2bb7b2b2a3bb2b3b3b4b5
ababab7a2abb6b2a3a2bb5b7b3a3bb4b6b4b5b5b6b7
bababa2babba3ba2bbab2b3ba3bba2babb3b4ba3ba2bb4ba3bb5b6b7
b2b2b7b3b6b2b2b4b5b7b7b3b5b6b6b2b6b7b7b2b3
a3a3b2a3bb7b3a3b5b6b2b2a3bb6b7b7b3b7b2b2b3b4
a2ba2ba2b6a3a2bb5b7b2a3bb4b6b2b3b3b5b3b4b4b5b6
ba2ba2ba3ba2bb3ba3bba2b7b2b4ba3ba2bb2b3b3ba3bb3b4b4b5b6
babbabbab2ba2babb7b3ba3ba2bb6b2b4ba3bb5b7b5b6b6b7b2
b3b3b2b4b7b3b3b5b6b2b2b4b6b7b7b3b7b2b2b3b4
a3ba3ba3b5b2a3bb4b6b7b3b3b5b7b2b2b4b2b3b3b4b5
ba3ba3b3ba3bb2b4ba3b6b7b3b3ba3bb7b2b2b4b2b3b3b4b5
ba2bba2bba2b7ba3ba2bb6b2b3ba3bb5b7b3b4b4b6b4b5b5b6b7
b4b4b3b5b2b4b4b6b7b3b3b5b7b2b2b4b2b3b3b4b5
ba3bba3bba3b6b3ba3bb5b7b2b4b4b6b2b3b3b5b3b4b4b5b6
b5b5b4b6b3b5b5b7b2b4b4b6b2b3b3b5b3b4b4b5b6
b6b6b5b7b4b6b6b2b3b5b5b7b3b4b4b6b4b5b5b6b7
b7b7b6b2b5b7b7b3b4b6b6b2b4b5b5b7b5b6b6b7b2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

28 unique, 65 total

Length:Presentation:Description:Related:
8 〈a, b | aab=a, bbbb=1〉 Finite non-commutative monoid with 20 elements 3 isomorphic, 1 anti-isomorphic
8 〈a, b | ab=aa, bbbb=1〉 Finite non-commutative monoid with 20 elements 1 isomorphic
9 〈a, b | abab=a, bbbb=1〉 Finite non-commutative monoid with 20 elements 2 isomorphic
9 〈a, b | aba=ab, bbbb=1〉 Finite non-commutative monoid with 20 elements 1 isomorphic, 1 anti-isomorphic
9 〈a, b | ab=aa, bbbb=b〉 Finite non-commutative monoid with 20 elements
10 〈a, b | abb=aab, aaaa=1〉 Finite non-commutative monoid with 20 elements 2 isomorphic
10 〈a, b | baa=abb, abab=1〉 Finite non-Abelian group with 20 elements 1 isomorphic, 1 anti-isomorphic
10 〈a, b | aaaaa=1, abbbb=1〉 Isomorphic to ℤ20 16 isomorphic
10 〈a, b | aab=bb, aaaa=a〉 Finite non-commutative monoid with 20 elements
10 〈a, b | aaa=bb, bab=aa〉 Finite non-commutative monoid with 20 elements 1 isomorphic
10 〈a, b | aba=b, aaaa=bb〉 Finite non-commutative monoid with 20 elements
10 〈a, b | ab=aa, bbbb=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaaa=aa, abbb=b〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaab=bb, bbba=a〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaaa=a, bbbbb=a〉 Finite commutative monoid with 20 elements
11 〈a, b | aaaa=b, bbbbb=a〉 Finite commutative monoid with 20 elements
11 〈a, b | aaaa=b, bbbbb=b〉 Finite commutative monoid with 20 elements
11 〈a, b | aab=ba, abbabb=1〉 Finite non-Abelian group with 20 elements 2 isomorphic
11 〈a, b | aba=bb, baaab=a〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aab=aa, baba=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=aa, aaaa=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=aa, aaab=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=bb, abb=aaa〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaaa=1, aaabab=b〉 Finite non-commutative monoid with 20 elements 1 isomorphic
11 〈a, b | aaaa=1, aabab=ab〉 Finite non-commutative monoid with 20 elements 1 isomorphic
11 〈a, b | aba=b, aaaaabb=1〉 Finite non-Abelian group with 20 elements 3 isomorphic
11 〈a, b | aab=a, bbbbb=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | ab=aa, bbbb=bbb〉 Finite non-commutative monoid with 20 elements