#1 ⟨a, b, c | aa=1, bc=1⟩

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Next:#2 ⟨a, b, c | ab=1, ac=1⟩

Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. a2 ⇒ 1 [1]
2. bc ⇒ 1 [2]
# abc:aa=1,bc=1 abc - -
aa=1
bc=1

Isomorphic instances

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

28 total

Σ#PresentationMapping
6161⟨a, b, c | aa=1, aabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
6164⟨a, b, c | aa=1, abca=1⟩φ(a) = a, φ(b) = b, φ(c) = c
6167⟨a, b, c | aa=1, baac=1⟩φ(a) = a, φ(b) = b, φ(c) = c
6214⟨a, b, c | aa=1, abc=a⟩φ(a) = a, φ(b) = b, φ(c) = c
6261⟨a, b, c | aa=1, bc=aa⟩φ(a) = a, φ(b) = b, φ(c) = c
82298⟨a, b, c | aaa=a, aabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82301⟨a, b, c | aaa=a, abca=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82414⟨a, b, c | aab=b, aabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82420⟨a, b, c | aab=b, abca=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82432⟨a, b, c | aab=b, baac=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82442⟨a, b, c | aab=b, bcaa=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82679⟨a, b, c | abc=a, aabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82689⟨a, b, c | abc=a, abca=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82719⟨a, b, c | abc=a, bcaa=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86113⟨a, b, c | aa=1, aaaabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86116⟨a, b, c | aa=1, aaabca=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86119⟨a, b, c | aa=1, aabaac=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86129⟨a, b, c | aa=1, aabcaa=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86140⟨a, b, c | aa=1, abaaca=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86193⟨a, b, c | aa=1, baaaac=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86618⟨a, b, c | aa=1, aaabc=a⟩φ(a) = a, φ(b) = b, φ(c) = c
86631⟨a, b, c | aa=1, aabca=a⟩φ(a) = a, φ(b) = b, φ(c) = c
86641⟨a, b, c | aa=1, abaac=a⟩φ(a) = a, φ(b) = b, φ(c) = c
87117⟨a, b, c | aa=1, aaaa=bc⟩φ(a) = a, φ(b) = b, φ(c) = c
87133⟨a, b, c | aa=1, aabc=aa⟩φ(a) = a, φ(b) = b, φ(c) = c
87173⟨a, b, c | aa=1, abca=aa⟩φ(a) = a, φ(b) = b, φ(c) = c
87200⟨a, b, c | aa=1, baac=aa⟩φ(a) = a, φ(b) = b, φ(c) = c
87622⟨a, b, c | aa=1, abc=aaa⟩φ(a) = a, φ(b) = b, φ(c) = c