#445 ⟨a, b, c | ac=ab, aaa=1⟩

Properties

Sum of relation sides is 7
Isomorphic to ℤ₃ ∗ ℕ
Infinite cancellative non-commutative monoid
Element a²b has infinite order
Submonoid of enveloping group: ⟨a, b | aaa⟩
- 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.	a³ ⇒ 1	[2]

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

2 unique, 54 total

Σ	#	Presentation	Properties	Description	φ
6	58	⟨a, b, c \| aaa=1, bcb=1⟩	Grp Inf	ℤ₃ ∗ ℤ	27
6	99	⟨a, b, c \| aa=b, ccc=1⟩	Can Inf	ℤ₃ ∗ ℕ	25

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

1 total

Σ	#	Presentation	Mapping
8	4105	⟨a, b, c \| aaa=1, aaab=c⟩	φ(a) = a, φ(b) = b, φ(c) = b