Abstract Algebra: Theory and Applications · Problem 14.5.25

The Sylow Theorems — Thomas Judson

Mathematics — Abstract Algebra · p-group-proper-subgroup

Problem

If GG is a group of order pnp^n, where pp is prime and n≥2n \geq 2, show that GG must have a proper subgroup of order pp. If n≥3n \geq 3, is it true that GG will have a proper subgroup of order p2p^2?

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