#609 ⟨a, b | aaaaabbba=1⟩

Properties

Sum of relation sides is 9
Infinite non-Abelian group
Element a⁴ba has infinite order
Inverses of generators:
- a^-1 = a⁵d
- b^-1 = b²c
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aaaaaabbb⟩
- Isomorphism: φ(a) = a, φ(b) = b

Format:	Pretty Plain
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:	Leftmost Rightmost
Result:	1 1

# ab:aaaaabbba=1 abcd aaaaaa=c,bbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
bbb=d
aaaaaa=c

3 unique, 3 total

Σ	#	Presentation	Properties
9	1008	⟨a, b \| aaaaaa=bbb⟩	Can Inf
10	2764	⟨a, b \| babab=aaaaa⟩	Can Inf
11	5406	⟨a, b \| abbabba=bbbb⟩	Can Inf

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

3 total

Σ	#	Presentation	Mapping
9	623	⟨a, b \| aaaabbbaa=1⟩	φ(a) = a, φ(b) = b
9	646	⟨a, b \| aaabbbaaa=1⟩	φ(a) = a, φ(b) = b
9	694	⟨a, b \| aabbbbbba=1⟩	φ(a) = b, φ(b) = a