= Torsion group construction by p-power relators
Enumerate all nonidentity words $w_i$ in the rank-two <free group> and impose relations $w_i^{p^{i+2}}=1$. The resulting two-generated <group> has
$$
\operatorname{def}_p\geq2-\sum_{i\geq1}p^{-(i+2)}=2-\frac1{p^2(p-1)}>1.
$$
It is infinite by <p-deficiency at least one implies infinitude>. Each element has order a power of $p$, so it is a <torsion group>. The infinitely many relators are essential to this particular construction; finite generation does not imply a <finite group presentation>.
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