- #1

jstrunk

- 55

- 2

- TL;DR Summary
- I can never do it

The book I am using has a number of exercises like this:

If G is a p-group, show that G cannot have exactly p+1 conjugacy classes.

If G is a p-group with p+2 conjugacy classes, show that the order of G is 4.

I can never solve any problem that involves connecting the number of conjugacy classes to the order of a p-group.

The author seems to think he showed how to do it, but if so, it went right over my head.

Please don't make me show my work.

I have spent a month on just these two problems and gotten nowhere and given myself mental block.

Is there any place I can find a clear explanation of this at a introductory level?

At the point I am in my book, Sylow subgroups have been introduced but we haven't done the Sylow Theorems yet,

so that should give you an idea of what I mean by an introductory level.

If G is a p-group, show that G cannot have exactly p+1 conjugacy classes.

If G is a p-group with p+2 conjugacy classes, show that the order of G is 4.

I can never solve any problem that involves connecting the number of conjugacy classes to the order of a p-group.

The author seems to think he showed how to do it, but if so, it went right over my head.

Please don't make me show my work.

I have spent a month on just these two problems and gotten nowhere and given myself mental block.

Is there any place I can find a clear explanation of this at a introductory level?

At the point I am in my book, Sylow subgroups have been introduced but we haven't done the Sylow Theorems yet,

so that should give you an idea of what I mean by an introductory level.