#555 ⟨a, b | abbba=bab⟩
Contents
- Properties
- Rewriting system
- Other submonoids of same group
- Sum of relation sides is 8
- Infinite cancellative non-commutative monoid
- Element a has infinite order
- Submonoid of enveloping group: ⟨a, b | aaabb⟩
-
Embedding: φ(a) = aabaabab, φ(b) = b-1a-1a-1
- Auxiliary generators:
- c = ab
- d = cb
- e = db
- Reduction order:
- Left-to-right shortlex with b < a < c < d < e
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:abbba=bab bacde ab=c,cb=d,db=e morph:2/1,2/1,2/0
ab=c
cb=d
db=e
ea=bc
ec=bd
ed=be
beb=ee
ceb=aee
deb=cee
eeb=dee
12 unique, 57 total
| Σ | # | Presentation | Properties | φ |
|---|
| 5 | 30 | ⟨a, b | aabba=1⟩ | Grp Inf | 40 |
| 5 | 43 | ⟨a, b | abba=b⟩ | Can Inf | |
| 5 | 46 | ⟨a, b | aaa=bb⟩ | Can Inf | |
| 5 | 53 | ⟨a, b | aba=bb⟩ | Can Inf | |
| 6 | 91 | ⟨a, b | ababa=b⟩ | Can Inf | 5 |
| 6 | 123 | ⟨a, b | bab=aba⟩ | Can Inf | |
| 7 | 267 | ⟨a, b | abba=bab⟩ | Can Inf | |
| 9 | 1137 | ⟨a, b | abbbba=bab⟩ | Can Inf | |
| 9 | 1262 | ⟨a, b | ababa=baab⟩ | Can Inf | |
| 10 | 2361 | ⟨a, b | abbbbba=bab⟩ | Can Inf | |
| 11 | 4887 | ⟨a, b | abbbbbba=bab⟩ | Can Inf | |
| 11 | 5855 | ⟨a, b | abaaba=baaab⟩ | Can Inf | |