#185 ⟨a, b, c | ab=1, abcc=1⟩

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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. ab ⇒ 1 [1]
2. c2 ⇒ 1 [2]
# abc:ab=1,abcc=1 abc - -
ab=1
cc=1

Isomorphic instances

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

24 total

Σ#PresentationMapping
6206⟨a, b, c | ab=1, cabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
6254⟨a, b, c | ab=1, bcc=b⟩φ(a) = a, φ(b) = b, φ(c) = c
6264⟨a, b, c | ab=1, cc=ab⟩φ(a) = a, φ(b) = b, φ(c) = c
82568⟨a, b, c | aba=a, abcc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82579⟨a, b, c | aba=a, bacc=1⟩φ(a) = b, φ(b) = a, φ(c) = c
82589⟨a, b, c | aba=a, cabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86301⟨a, b, c | ab=1, aabbcc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86345⟨a, b, c | ab=1, ababcc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86375⟨a, b, c | ab=1, abcabc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86387⟨a, b, c | ab=1, abccab=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86574⟨a, b, c | ab=1, caabbc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86580⟨a, b, c | ab=1, cababc=1⟩φ(a) = a, φ(b) = b, φ(c) = c
86876⟨a, b, c | ab=1, abbcc=b⟩φ(a) = a, φ(b) = b, φ(c) = c
86892⟨a, b, c | ab=1, abcca=a⟩φ(a) = a, φ(b) = b, φ(c) = c
86985⟨a, b, c | ab=1, babcc=b⟩φ(a) = a, φ(b) = b, φ(c) = c
87047⟨a, b, c | ab=1, bcabc=b⟩φ(a) = a, φ(b) = b, φ(c) = c
87303⟨a, b, c | ab=1, aabb=cc⟩φ(a) = a, φ(b) = b, φ(c) = c
87347⟨a, b, c | ab=1, abab=cc⟩φ(a) = a, φ(b) = b, φ(c) = c
87390⟨a, b, c | ab=1, abcc=ab⟩φ(a) = a, φ(b) = b, φ(c) = c
87536⟨a, b, c | ab=1, bbcc=bb⟩φ(a) = a, φ(b) = b, φ(c) = c
87562⟨a, b, c | ab=1, bcca=ba⟩φ(a) = a, φ(b) = b, φ(c) = c
87584⟨a, b, c | ab=1, cabc=ab⟩φ(a) = a, φ(b) = b, φ(c) = c
87801⟨a, b, c | ab=1, bcc=abb⟩φ(a) = a, φ(b) = b, φ(c) = c
87807⟨a, b, c | ab=1, bcc=bab⟩φ(a) = a, φ(b) = b, φ(c) = c