#6101 ⟨a, b | aab=a, bbbbbb=1⟩

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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. a7 ⇒ a
  2. ab ⇒ a6
  3. b6 ⇒ 1 
# ab:aab=a,bbbbbb=1 a/b
aaaaaaa=a
ab=aaaaaa
bbbbbb=1

Right Cayley graph

Left Cayley graph

Others with same cardinality

2 unique, 9 total

Σ#PresentationDescriptionRelated
1114981⟨a, b | aaa=bb, aabaab=1⟩Finite non-Abelian group with 42 elements7 iso
1120647⟨a, b | ab=aa, bbbbbb=b⟩Finite non-commutative monoid with 42 elements

Other isomorphic instances

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

3 total

Σ#PresentationMapping
106909⟨a, b | ab=aa, bbbbbb=1⟩φ(a) = a, φ(b) = bbbbb
1114256⟨a, b | abab=a, bbbbbb=1⟩φ(a) = aa, φ(b) = b
1115364⟨a, b | aba=ab, bbbbbb=1⟩φ(a) = ba, φ(b) = b