#275 ⟨a, b | aaaaabba=1⟩

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Quick links

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

Properties

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
#RuleProof
1. b2 ⇒ d [3]
2. ca ⇒ ac [6]
3. cb ⇒ bc [15]
4. cd ⇒ 1 [9]
5. da ⇒ ad [13]
6. db ⇒ bd [5]
7. dc ⇒ 1 [14]
8. a6 ⇒ c [2]
# ab:aaaaabba=1 abcd aaaaaa=c,bb=d magic:0
bb=d
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaaaa=c

Other submonoids of same group

6 unique, 6 total

Σ#PresentationDescriptionRelated
8412⟨a, b | abbbbba=b⟩Infinite cancellative non-commutative monoid
8415⟨a, b | aaaaaa=bb⟩Infinite cancellative non-commutative monoid
8484⟨a, b | abbbba=bb⟩Infinite cancellative non-commutative monoid
8489⟨a, b | aaaaa=bab⟩Infinite cancellative non-commutative monoid
8556⟨a, b | abbba=bbb⟩Infinite cancellative non-commutative monoid
8585⟨a, b | baab=aaaa⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

7 total

Σ#PresentationMapping
8281⟨a, b | aaaabbaa=1⟩φ(a) = a, φ(b) = b
8292⟨a, b | aaabbaaa=1⟩φ(a) = a, φ(b) = b
8340⟨a, b | abbbbbba=1⟩φ(a) = b, φ(b) = a
101285⟨a, b | aaaaaababa=1⟩φ(a) = a, φ(b) = aaaaadb
101295⟨a, b | aaaaababaa=1⟩φ(a) = a, φ(b) = aaaaadb
101314⟨a, b | aaaababaaa=1⟩φ(a) = a, φ(b) = aaaaadb
101475⟨a, b | abaaaaaaab=1⟩φ(a) = a, φ(b) = aaaaadb