Essential Group Theory by Batty Michael

Author:Batty, Michael [Batty, Michael]
Language: eng
Format: epub
Publisher: UNKNOWN
Published: 2021-04-23T16:00:00+00:00

-subgroups of a group then

1. If

is a Sylow

-subgroup of

then

divides the index . 2.

.

Exercise 11.8 What are the Sylow

-subgroups of the dihedral groups and ?

Exercise 11.9 Let

be a group such that the order of

only has two prime divisors, and , with . Let

be a

-Sylow subgroup of

and let

Suppose that

is the only

-Sylow subgroup of

.

be a

-Sylow subgroup. Show that . and

is the only

-Sylow subgroup. Show that

Exercise 11.10 Find a

-Sylow subgroup and a

-Sylow subgroup of .

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