#3138 ⟨a, b, c | ac=ab, aaaa=1⟩

Properties

Sum of relation sides is 8
Isomorphic to ℤ₄ ∗ ℕ
Infinite cancellative non-commutative monoid
Element a³b has infinite order
Submonoid of enveloping group: ⟨a, b | aaaa⟩
- Embedding: φ(a) = a, φ(b) = b, φ(c) = 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

#	Rule	Proof
1.	c ⇒ b	[3]
2.	a⁴ ⇒ 1	[2]

# abc:ac=ab,aaaa=1 abc - -
c=b
aaaa=1

2 unique, 21 total

Σ	#	Presentation	Properties	Description	φ
7	679	⟨a, b, c \| aba=1, cccc=1⟩	Grp Inf	ℤ₄ ∗ ℤ	11
7	774	⟨a, b, c \| aa=b, cccc=1⟩	Can Inf	ℤ₄ ∗ ℕ	8