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〈a, b | aba=bb, abb=aaa〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. a6 ⇒ a4
  2. a4b ⇒ a4
  3. a2ba ⇒ a3
  4. ba4 ⇒ a4
  5. b2 ⇒ aba
  6. ba3b ⇒ a5
  7. (ba)2 ⇒ (ab)2

Idempotents

2 elements

Cayley table

Idempotents are shown in bold.

1aba2abbaa3a2bababa2baba4a3ba2baba3ba2b(ba)2a5a3baba2ba
11aba2abbaa3a2bababa2baba4a3ba2baba3ba2b(ba)2a5a3baba2ba
aaa2aba3a2babaa4a3ba2baa3(ba)2a5a4a3baa4a3bba3a4a5a3ba
bbbaababa2baba3ba3ba2b(ba)2a4a3ba4a5ba2baa5a4a3baa5a4a5
a2a2a3a2ba4a3ba2baa5a4a3baa4ba3a4a5a5a5a4a4a5a4a5
abababaa2baa3(ba)2a4a4a3bba3a5a4a5a4a3baa4a5a5a4a5a4
bababa2babba3ba2b(ba)2a4a5ba2baba3a3baa5a4a4a4a5a5a4a5a4
a3a3a4a3ba5a4a3baa4a5a5a5a4a5a4a4a4a5a5a4a5a4
a2ba2ba2baa3baa4ba3a5a5a4a4a4a5a4a5a5a5a4a4a5a4a5
abaabaa3(ba)2a4a3bba3a5a4a3baa4a5a4a5a5a5a4a4a5a4a5
ba2ba2ba3ba2ba4a5ba2baa5a4a4a4a5a4a5a5a5a4a4a5a4a5
babbab(ba)2ba2baba3a3baa4a4a5a5a5a4a5a4a4a4a5a5a4a5a4
a4a4a5a4a4a5a5a5a4a4a4a5a4a5a5a5a4a4a5a4a5
a3ba3ba3baa5a5a4a4a4a5a5a5a4a5a4a4a4a5a5a4a5a4
a2baa2baa4ba3a5a4a4a4a5a5a5a4a5a4a4a4a5a5a4a5a4
ba3ba3a4a5a5a4a4a4a5a5a5a4a5a4a4a4a5a5a4a5a4
ba2bba2bba2baa4a4a5a5a5a4a4a4a5a4a5a5a5a4a4a5a4a5
(ba)2(ba)2ba3a3baa4a5a5a5a4a4a4a5a4a5a5a5a4a4a5a4a5
a5a5a4a5a5a4a4a4a5a5a5a4a5a4a4a4a5a5a4a5a4
a3baa3baa5a4a4a5a5a5a4a4a4a5a4a5a5a5a4a4a5a4a5
ba2baba2baa4a5a5a4a4a4a5a5a5a4a5a4a4a4a5a5a4a5a4

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=a, aaaa=bb〉 Finite non-commutative monoid with 20 elements
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 | 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