5.6. ADDITIONAL EXERCISES FOR CHAPTER 5
263
5.6.17.
Let
G
be a finite group,
p
a prime, and
P
a
p
–Sylow subgroup.
Suppose
H
is a
normal
subgroup of
G
of order
p
k
for some
k
. Show that
H
P
.
5.6.18.
Show that a group of order
2
n
5
m
,
m; n
1
, has a normal
5
–Sylow
subgroup. Can you generalize this statement?
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 Fall '08
 EVERAGE
 Algebra, Group Theory, Addition, Normal subgroup, Abelian group, Subgroup, Index of a subgroup

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