#11604 ⟨a, b | baabb=a, bbbbb=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. b5 ⇒ 1
  2. a2 ⇒ b4ab3
  3. aba ⇒ b2ab
  4. bab2a ⇒ (ab4)2
  5. bab4a ⇒ ab3ab2
  6. (b3a)2 ⇒ ab2ab4 
# ab:baabb=a,bbbbb=1 b/a
bbbbb=1
aa=bbbbabbb
aba=bbab
babba=abbbbabbbb
babbbba=abbbabb
bbbabbba=abbabbbb

Right Cayley graph

Left Cayley graph

Others with same cardinality

1 unique, 34 total

Σ#PresentationDescriptionRelated
91385⟨a, b | aaba=b, bbbb=1⟩Finite non-Abelian group with 60 elements28 iso, 5 anti-iso

Other isomorphic instances

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

3 total

Σ#PresentationMapping
1111916⟨a, b | aaba=bb, aaaaa=1⟩φ(a) = b, φ(b) = ab
1111996⟨a, b | aabb=ba, aaaaa=1⟩φ(a) = bbb, φ(b) = a
1112824⟨a, b | baa=abb, aaaaa=1⟩φ(a) = bbb, φ(b) = ab