An infinite finitely presented residually finite 2-group and a finitely presented nil algebra

Constructs an infinite finitely presented residually finite group whose elements all have finite 2-power order, answering the finitely presented Burnside problem negatively even in this class. The construction also yields an infinite-dimensional finitely presented nil associative 𝔽₂-algebra and a finitely presented infinite-dimensional algebraic unitization, giving negative answers to the corresponding nilpotence and Kurosh finiteness questions.