#704 ⟨a, b | abaabaaba=1⟩

Properties

Sum of relation sides is 9
Isomorphic to ℤ₃ ∗ ℤ
Infinite non-Abelian group
Element a has infinite order
Inverses of generators:
- a^-1 = ab(a²b)²
- b^-1 = a²(ba²)²
Reduced group presentation: ⟨a, b | aaa⟩
- Isomorphism: φ(a) = b, φ(b) = b^-1b^-1a

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

#	Rule	Proof
1.	b(a²b)²a ⇒ ab(a²b)²	[2]
2.	(a²b)³ ⇒ 1	[4]

# ab:abaabaaba=1 ab - -
baabaaba=abaabaab
aabaabaab=1

1 unique, 1 total

Σ	#	Presentation	Properties	Description
3	3	⟨a, b \| aaa=1⟩	Can Inf	ℤ₃ ∗ ℕ