Kostrikin's theorem on restricted Burnside problem

Statement

Let $p$ be a prime number and $d$ any natural number. Then, the restricted Burnside group $RB(d,p)$ is a finite group. In other words, the answer to the restricted Burnside problem is yes for all prime numbers.

Facts used

1. Exponent p implies associated Lie ring is (p-1)-Engel Lie algebra over field of p elements
2. Minimum size of generating set of associated Lie ring equals minimum size of generating set of quotient of group by nilpotent residual
3. Kostrikin's theorem on Engel Lie rings
4. Reduction of restricted Burnside problem to associated Lie ring

Proof

Given: A prime number $p$, a natural number $d$

To prove: The restricted Burnside group $RB(d,p)$ is a finite group

Proof: Denote by $B(d,p)$ the Burnside group and by $L(B(d,p))$ the associated Lie ring to the Burnside group.

Step no.	Assertion/construction	Facts used	Given data used	Previous steps used	Explanation
1	$L(B(d,p))$ is a $(p-1)$-Engel Lie ring that is also an algebra over the field of $p$ elements.	Fact (1)			Fact-direct
2	$L(B(d,p))$ is finitely generated	Fact (2)	$B(d,p)$, by definition, is generated by a set of size $d$
3	$L(B(d,p))$ is nilpotent	Fact (3)		Steps (1), (2)	Step-fact combination direct
4	$RB(d,p)$ is finite	Fact (4)		Step (3)	Step-fact combination direct