#1810 ⟨a, b | abbababba=b

Quick links

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

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. cbc ⇒ b [3]
2. ab2a ⇒ c [2]
3. ab2c ⇒ b2ca [5]
4. cb2 ⇒ b2c [4]
5. ab3 ⇒ b2cabc [6]
# ab:abbababba=b ac/b abba=c morph:4/0
cbc=b
abba=c
abbc=bbca
cbb=bbc
abbb=bbcabc

Other submonoids of same group

3 unique, 5 total

Σ#PresentationDescriptionRelated
8315a, b | aabbabba=1⟩Infinite non-Abelian group2 iso
8471a, b | abaaba=bbInfinite cancellative non-commutative monoid
102303a, b | abaaaba=babInfinite cancellative non-commutative monoid