#950 ⟨a, b | ab=a, bbbb=a⟩

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Properties

Element profile

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. b5 ⇒ b4
  2. a ⇒ b4 
# ab:ab=a,bbbb=a b/a
bbbbb=bbbb
a=bbbb

Staircase diagram

Cayley table

Idempotents are shown in bold.

1bb2b3b4
11bb2b3b4
bbb2b3b4b4
b2b2b3b4b4b4
b3b3b4b4b4b4
b4b4b4b4b4b4

Right Cayley graph

Idempotents are shown in bold.

Others with same cardinality

11 unique, 1430 total

Σ#PresentationDescriptionRelated
644⟨a, b | aa=b, abb=1⟩Isomorphic to ℤ51132 iso
7253⟨a, b | aa=b, abb=a⟩Isomorphic to ℕ(5 = 1)71 iso
7254⟨a, b | aa=b, abb=b⟩Isomorphic to ℕ(5 = 2)43 iso
7268⟨a, b | ab=a, baa=b⟩Finite non-commutative monoid with 5 elements63 iso, 23 anti-iso
8574⟨a, b | aaa=b, aab=b⟩Isomorphic to ℕ(5 = 3)27 iso
8995⟨a, b | ab=a, aaa=bb⟩Finite commutative monoid with 5 elements19 iso
81019⟨a, b | ab=a, bba=bb⟩Finite non-commutative monoid with 5 elements25 iso
81020⟨a, b | ab=a, bbb=aa⟩Finite commutative monoid with 5 elements9 iso
81022⟨a, b | ab=a, bbb=ba⟩Finite non-commutative monoid with 5 elements4 iso
108617⟨a, b | aa=a, abbbba=b⟩Finite commutative monoid with 5 elements3 iso
1115426⟨a, b | aaa=aa, abbba=b⟩Finite commutative monoid with 5 elements

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

32 total

Σ#PresentationMapping
8985⟨a, b | aa=b, abb=bb⟩φ(a) = b, φ(b) = bb
8988⟨a, b | aa=b, bab=bb⟩φ(a) = b, φ(b) = bb
91688⟨a, b | abb=ab, bbb=a⟩φ(a) = bbb, φ(b) = b
91690⟨a, b | abb=ba, bbb=a⟩φ(a) = bbb, φ(b) = b
91696⟨a, b | bab=ab, bbb=a⟩φ(a) = bbb, φ(b) = b
93042⟨a, b | aa=b, aaab=bb⟩φ(a) = b, φ(b) = bb
93046⟨a, b | aa=b, aaba=bb⟩φ(a) = b, φ(b) = bb
93133⟨a, b | ab=a, bbbb=ab⟩φ(a) = bbbb, φ(b) = b
93158⟨a, b | aa=b, abb=aab⟩φ(a) = b, φ(b) = bb
93159⟨a, b | aa=b, abb=aba⟩φ(a) = b, φ(b) = bb
93161⟨a, b | aa=b, baa=abb⟩φ(a) = b, φ(b) = bb
93163⟨a, b | aa=b, bab=aab⟩φ(a) = b, φ(b) = bb
93164⟨a, b | aa=b, bab=aba⟩φ(a) = b, φ(b) = bb
108914⟨a, b | aa=b, aaaaa=bb⟩φ(a) = b, φ(b) = bb
109187⟨a, b | aa=b, aaaa=abb⟩φ(a) = b, φ(b) = bb
109188⟨a, b | aa=b, aaaa=bab⟩φ(a) = b, φ(b) = bb
109191⟨a, b | aa=b, aaab=aab⟩φ(a) = b, φ(b) = bb
109192⟨a, b | aa=b, aaab=aba⟩φ(a) = b, φ(b) = bb
109194⟨a, b | aa=b, aaab=baa⟩φ(a) = b, φ(b) = bb
109199⟨a, b | aa=b, aaba=aab⟩φ(a) = b, φ(b) = bb
109200⟨a, b | aa=b, aaba=aba⟩φ(a) = b, φ(b) = bb
109202⟨a, b | aa=b, aaba=baa⟩φ(a) = b, φ(b) = bb
109379⟨a, b | ab=a, bbbb=abb⟩φ(a) = bbbb, φ(b) = b
1114370⟨a, b | aaaa=b, aaaaa=b⟩φ(a) = b, φ(b) = bbbb
1119305⟨a, b | aaa=b, aaaaa=ab⟩φ(a) = b, φ(b) = bbb
1119849⟨a, b | aaa=b, aaaa=aab⟩φ(a) = b, φ(b) = bbb
1119850⟨a, b | aaa=b, aaaa=aba⟩φ(a) = b, φ(b) = bbb
1125261⟨a, b | aa=b, aaaaa=aab⟩φ(a) = b, φ(b) = bb
1125262⟨a, b | aa=b, aaaaa=aba⟩φ(a) = b, φ(b) = bb
1125726⟨a, b | aa=b, aaab=aaaa⟩φ(a) = b, φ(b) = bb
1125727⟨a, b | aa=b, aaba=aaaa⟩φ(a) = b, φ(b) = bb
1125904⟨a, b | ab=a, bbbb=abbb⟩φ(a) = bbbb, φ(b) = b