#10273 ⟨a, b | aa=1, ababa=bbb⟩

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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. a2 ⇒ 1
  2. (ba)2 ⇒ ab3
  3. b3a ⇒ (ab)2
  4. b2ab3 ⇒ abab2a
  5. bab7 ⇒ aba(b2a)2
  6. b10 ⇒ a(b2a)3
  7. ba(b2a)3 ⇒ a(b2a)3b 
# ab:aa=1,ababa=bbb ab
aa=1
baba=abbb
bbba=abab
bbabbb=ababba
babbbbbbb=ababbabba
bbbbbbbbbb=abbabbabba
babbabbabba=abbabbabbab

Right Cayley graph

Left Cayley graph

Others with same cardinality

2 unique, 10 total

Σ#PresentationDescriptionRelated
91523⟨a, b | aab=ba, bbbb=1⟩Finite non-commutative monoid with 64 elements6 iso
105442⟨a, b | aaaa=1, ababbb=1⟩Finite non-Abelian group with 64 elements2 iso

Other isomorphic instances

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

5 total

Σ#PresentationMapping
1010294⟨a, b | aa=1, abbba=bab⟩φ(a) = a, φ(b) = b
1010511⟨a, b | aa=1, baba=abbb⟩φ(a) = a, φ(b) = b
1127113⟨a, b | aa=1, abababa=bb⟩φ(a) = a, φ(b) = ab
1127640⟨a, b | aa=1, ababab=bba⟩φ(a) = a, φ(b) = ab
1128255⟨a, b | aa=1, babab=abba⟩φ(a) = a, φ(b) = ab