#1174 ⟨a, b | aaaba=baab⟩

Up:Monoid enumeration
Prev:#1173 ⟨a, b | aaaba=baaa⟩
Next:#1175 ⟨a, b | aaaba=baba⟩

Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

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. a3ba ⇒ ba2b [1]
2. a3b2a2b ⇒ b(a2b)2a [2]
# ab:aaaba=baab ba - -
aaaba=baab
aaabbaab=baabaaba

Other submonoids of same group

6 unique, 24 total

Σ#PresentationPropertiesφ
7207⟨a, b | aaaba=bb⟩Can Inf
8504⟨a, b | aaaba=bab⟩Can Inf
9670⟨a, b | aabababba=1⟩Grp Inf18
9850⟨a, b | abababba=b⟩Can Inf
114828⟨a, b | abababba=bab⟩Can Inf
115942⟨a, b | abbbba=babbb⟩Can Inf

Other submonoids of anti-isomorphic group

6 unique, 6 total

Σ#PresentationProperties
7174⟨a, b | aaabba=b⟩Can Inf
8362⟨a, b | aaababa=b⟩Can Inf
9765⟨a, b | aaabaaba=b⟩Can Inf
101612⟨a, b | aaabaaaba=b⟩Can Inf
102742⟨a, b | baaab=aaaba⟩Can Inf
113430⟨a, b | aaabaaaaba=b⟩Can Inf