#138 ⟨a, b, c | aa=b, ab=c⟩

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Contents

  1. Properties
  2. Commutative structure
  3. Rewriting system
  4. Other submonoids of same group
  5. Isomorphic instances

Properties

Commutative structure

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. b ⇒ a2 [1]
2. c ⇒ a3 [2]
# abc:aa=b,ab=c a/bc - -
b=aa
c=aaa

Other submonoids of same group

1 unique, 1256 total

Σ#PresentationPropertiesDescriptionφ
43⟨a, b, c | ab=1, bc=1⟩Grp Com Infℤ1255

Isomorphic instances

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

26 total

Σ#PresentationMapping
6142⟨a, b, c | aa=b, bb=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaa
7901⟨a, b, c | aa=b, aaa=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaa
7902⟨a, b, c | aa=b, aab=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaa
7906⟨a, b, c | aa=b, aba=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaa
7907⟨a, b, c | aa=b, abb=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaa
7920⟨a, b, c | aa=b, bab=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaa
7924⟨a, b, c | aa=b, bbb=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaaa
7940⟨a, b, c | aa=b, ccc=a⟩φ(a) = aaa, φ(b) = aaaaaa, φ(c) = a
71009⟨a, b, c | ab=c, aaa=b⟩φ(a) = a, φ(b) = aaa, φ(c) = aaaa
82816⟨a, b, c | aaa=b, aab=c⟩φ(a) = a, φ(b) = aaa, φ(c) = aaaaa
82820⟨a, b, c | aaa=b, aba=c⟩φ(a) = a, φ(b) = aaa, φ(c) = aaaaa
82821⟨a, b, c | aaa=b, abb=c⟩φ(a) = a, φ(b) = aaa, φ(c) = aaaaaaa
82834⟨a, b, c | aaa=b, bab=c⟩φ(a) = a, φ(b) = aaa, φ(c) = aaaaaaa
82838⟨a, b, c | aaa=b, bbb=c⟩φ(a) = a, φ(b) = aaa, φ(c) = aaaaaaaaa
85159⟨a, b, c | aa=b, aaaa=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaa
85160⟨a, b, c | aa=b, aaab=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaa
85164⟨a, b, c | aa=b, aaba=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaa
85165⟨a, b, c | aa=b, aabb=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaaa
85178⟨a, b, c | aa=b, abab=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaaa
85182⟨a, b, c | aa=b, abba=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaaa
85183⟨a, b, c | aa=b, abbb=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaaaa
85217⟨a, b, c | aa=b, baab=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaaa
85221⟨a, b, c | aa=b, babb=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaaaa
85234⟨a, b, c | aa=b, bbbb=c⟩φ(a) = a, φ(b) = aa, φ(c) = aaaaaaaa
85271⟨a, b, c | aa=b, cccc=a⟩φ(a) = aaaa, φ(b) = aaaaaaaa, φ(c) = a
85486⟨a, b, c | ab=c, aaaa=b⟩φ(a) = a, φ(b) = aaaa, φ(c) = aaaaa