Hi everybody!(adsbygoogle = window.adsbygoogle || []).push({});

Question #1

What is the definition of a Klein group? The [tex]K_4[/tex] group has a table that looks like this:

[tex]

\begin{array}{c|cccc}

*&e&a&b&c \\\hline

e&e&a&b&c\\

a&a&e&c&b\\

b&b&c&e&a\\

c&c&b&a&e

\end{array}

[/tex]

What is the strict definition of a Klein group? That every element generates the entire group? Is [tex]\langle \lbrace 1, 3, 5, 7 \rbrace, +\rangle[/tex] a Klein group?

Question #2

All subgroups of the cyclic group [tex]C_{24}[/tex] are cyclic groups [tex]C_n[/tex] where [tex]n \mid 24[/tex]. So to find all subgroups, one can locate all divisors for 24. Correct?

This is what I do not understand: The subgroups of [tex]C_24[/tex] with the order 24 is [tex]c, c^5, c^7, c^{11}, c^{13}, c^{17}, c^{19}, c^{23}[/tex]. What does [tex]c^n[/tex] mean? Does [tex]c^n[/tex] generate [tex]\frac{24}{\gcd(24, n)}[/tex] elements?

I would really, really appreciate some help with this!

Thanks in advance,

Nille

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Klein and Cyclic group

**Physics Forums | Science Articles, Homework Help, Discussion**