#1446 ⟨a, b | aabbaabbba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = da2
- b-1 = b2cb2a2
- c-1 = d
- d-1 = c
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
- Auxiliary generator: aaa=c
- Auxiliary generator: bbaabbb=d
- cd ⇒ 1
- dc ⇒ 1
- ac ⇒ ca
- ad ⇒ da
- a3 ⇒ c
- cb2a2b ⇒ bcb2a2
- dbcb2 ⇒ b2a2bda
- ab2a2b ⇒ b3c
- abcb2 ⇒ cb3a
- a2b3 ⇒ bcb2da2
- db2cb2 ⇒ b2a2b2da
- ab2cb2 ⇒ cb3cbda
- b3cb2 ⇒ da
- cb2ab3 ⇒ (b2c)2abd
- cb2cab3 ⇒ bcb2ca2b2da2
- ab2ab3 ⇒ b3cba2bd
- ab2cab3 ⇒ b3c2b2da2
# ab:aabbaabbba=1 cda/b aaa=c,bbaabbb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
cbbaab=bcbbaa
dbcbb=bbaabda
abbaab=bbbc
abcbb=cbbba
aabbb=bcbbdaa
dbbcbb=bbaabbda
abbcbb=cbbbcbda
bbbcbb=da
cbbabbb=bbcbbcabd
cbbcabbb=bcbbcaabbdaa
abbabbb=bbbcbaabd
abbcabbb=bbbccbbdaa
Right Cayley graph (truncated)
Left Cayley graph (truncated)
Other isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1530 | ⟨a, b | abbaaabbba=1⟩ | φ(a) = b, φ(b) = a |
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 | 1461 | ⟨a, b | aabbbaabba=1⟩ | φ(a) = a, φ(b) = b |