#5073 ⟨a, b | aaa=ab, bbbb=b⟩

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Properties

Elements

Elements in the center commute with all other elements.
An idempotent element x satisfies x2 = x.
The index and period of x is the least m (index) and n (period) such that x(m+n) = xm.

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. a9 ⇒ a3
  2. ab ⇒ a3
  3. b4 ⇒ b 
# ab:aaa=ab,bbbb=b a/b
aaaaaaaaa=aaa
ab=aaa
bbbb=b

Right Cayley graph

Left Cayley graph

Others with same cardinality

4 unique, 40 total

Σ#PresentationDescriptionRelated
91345⟨a, b | aaab=a, bbbb=1⟩Finite non-commutative monoid with 36 elements5 iso, 8 anti-iso
92300⟨a, b | aaa=1, ababbb=1⟩Finite non-Abelian group with 36 elements23 iso
1116044⟨a, b | aaa=ab, bbbb=bb⟩Finite non-commutative monoid with 36 elements
1118959⟨a, b | aab=a, bbbbbb=b⟩Finite non-commutative monoid with 36 elements

Other isomorphic instances

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

1 total

Σ#PresentationMapping
1112995⟨a, b | abb=aaa, bbbb=b⟩φ(a) = a, φ(b) = bb