Special and General Linearity

Algebra Level 4

Let F q \mathbb{F}_q be the field with q q elements and for n 1 n \ge 1 , Let GL n ( F q ) \text{GL}_n(\mathbb{F}_q) represent the General linear group and SL n ( F q ) \text{SL}_n(\mathbb{F}_q) be the Special linear group of n × n n \times n matrices then which of the following is true?

A \mid A \mid represents the number of elements in A A Provide/Write a legitimate solution whatever the answer may be

S L n ( F q ) = 1 q 2 G L n ( F q ) . \mid SL_n(F_q) \mid=\frac{1}{q-2} \mid GL_n(F_q) \mid . S L n ( F q ) = 1 q 1 G L n ( F q ) . \mid SL_n(F_q) \mid=\frac{1}{q-1} \mid GL_n(F_q) \mid. G L n ( F q ) = 1 q S L n ( F q ) . \mid GL_n(F_q) \mid =\frac{1}{q} \mid SL_n(F_q) \mid . S L n ( F q ) = 1 q 3 G L n ( F q ) . \mid SL_n(F_q) \mid =\frac{1}{q-3} \mid GL_n(F_q) \mid . S L n ( F q ) = 1 q G L n ( F q ) . \mid SL_n(F_q) \mid = \frac{1}{q} \mid GL_n(F_q) \mid . S L n ( F q ) = 1 q 2 G L n ( F q ) . \mid SL_n(F_q) \mid = \frac{1}{q^2} \mid GL_n(F_q) \mid .

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

0 solutions

No explanations have been posted yet. Check back later!

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...