#3592 ⟨a, b, c | ba=ac, ca=ab⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaba^-1a^-1b^-1⟩
- Embedding: φ(a) = a, φ(b) = ab^-1a^-1, φ(c) = b^-1

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.	ba ⇒ ac	[1]
2.	ca ⇒ ab	[2]

# abc:ba=ac,ca=ab abc - -
ba=ac
ca=ab

8 unique, 16 total

Σ	#	Presentation	Properties	φ
7	533	⟨a, b, c \| ba=ab, cc=a⟩	Can Inf
8	2199	⟨a, b, c \| aabc=1, acba=1⟩	Grp Inf	5
8	2976	⟨a, b, c \| aab=c, baa=c⟩	Can Inf	2
8	3072	⟨a, b, c \| abc=b, cba=b⟩	Can Inf
8	3431	⟨a, b, c \| ba=ab, cac=b⟩	Can Inf
8	3587	⟨a, b, c \| ba=ab, cc=ab⟩	Can Inf	1
8	3596	⟨a, b, c \| ba=ac, cc=bb⟩	Can Inf
8	6088	⟨a, b, c \| ab=c, bca=cc⟩	Can Inf