Abstract Algebra: Theory and Applications · Problem 15.4.18

Rings — Thomas Judson

Mathematics — Abstract Algebra · sylow-theorems

Problem

Let

G

have order

p_1^{e_1} \cdots p_n^{e_n}

and suppose that

G

has

n

Sylow

p

-subgroups

P_1, \ldots, P_n

where

|P_i| = p_i^{e_i}

. Prove that

G

is isomorphic to

P_1 \times \cdots \times P_n