#3978 ⟨a, b, c | aba=1, ccccc=1⟩

Properties

Sum of relation sides is 8
Isomorphic to ℤ₅ ∗ ℤ
Infinite non-Abelian group
Element a has infinite order
Inverses of generators:
- a^-1 = ab
- b^-1 = a²
- c^-1 = c⁴
Reduced group presentation: ⟨a, b | aaaaa⟩
- Isomorphism: φ(a) = b, φ(b) = b^-1b^-1, φ(c) = a

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

# abc:aba=1,ccccc=1 abc - -
ba=ab
aab=1
ccccc=1

1 unique, 2 total

Σ	#	Presentation	Properties	Description	φ
8	4771	⟨a, b, c \| aa=b, ccccc=1⟩	Can Inf	ℤ₅ ∗ ℕ	1