#1448 ⟨a, b | aabbabaaba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = dbcba
- b-1 = cdbc
- c-1 = dbcb
- d-1 = (bc)2
Complete rewriting system
- Reduction order:
- Right-to-left recursive path with deg(b) = deg(c) = deg(d) = 0, b < c < d; deg(a) = 1
- Auxiliary generator: aa=c
- Auxiliary generator: abba=d
- bcd ⇒ dbc
- cdbcb ⇒ 1
- d(bc)2 ⇒ 1
- ac ⇒ ca
- ad ⇒ cb2a
- ab2 ⇒ d2bcba
- abc ⇒ cdbc2db(bc)2ab
- abd ⇒ dcb3cbcab
- a2 ⇒ c
# ab:aabbabaaba=1 reversed:bcd/a aa=c,abba=d frequency:2/2,4/3
bcd=dbc
cdbcb=1
dbcbc=1
ac=ca
ad=cbba
abb=ddbcba
abc=cdbccdbbcbcab
abd=dcbbbcbcab
aa=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
Other anti-isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1529 | ⟨a, b | abbaaabaab=1⟩ | φ(a) = a, φ(b) = b |