#1356 ⟨a, b | aaabababba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = a3d
- b-1 = cb(ab)2
- c-1 = d
- d-1 = c
Complete rewriting system
- Reduction order:
- Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
- Auxiliary generator: aaaa=c
- Auxiliary generator: bababb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a4 ⇒ c
- bcba ⇒ ab2c
- b2a3 ⇒ a3dbcb
- bab2c ⇒ a2(ab)3
- b(ab)2d ⇒ adbab2
- bab2ac ⇒ a3(ba)3
- (ba)3d ⇒ adbab2a
- bab2a2c ⇒ a3(ba)3a
- (ba)3ad ⇒ adbab2a2
- (ba)3a2 ⇒ adb(bc)2
- (ba)2b2 ⇒ d
- (b2c)2 ⇒ a3dba3cb(ab)2
- b2cb2ac ⇒ a3dba3c(ba)3
- b2cb2a2c ⇒ a3dba3c(ba)3a
# ab:aaabababba=1 reversed:cda/b aaaa=c,bababb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
bcba=abbc
bbaaa=aaadbcb
babbc=aaababab
bababd=adbabb
babbac=aaabababa
bababad=adbabba
babbaac=aaabababaa
bababaad=adbabbaa
bababaaa=adbbcbc
bababb=d
bbcbbc=aaadbaaacbabab
bbcbbac=aaadbaaacbababa
bbcbbaac=aaadbaaacbababaa
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 | 1423 | ⟨a, b | aabababbaa=1⟩ | φ(a) = a, φ(b) = b |
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 | 1373 | ⟨a, b | aaabbababa=1⟩ | φ(a) = a, φ(b) = b |