# about union of conjugate proper subgroups in a math paper

My question is about the shaded area in this image. Does the symbol $L=\bigcup_{g \in G} T^{g}$ means that $L$ is a union of sets or $L=\langle T^{g}, g\in G \rangle$? If it means the first one, then how did the authors prove that $L$ equals to that union? If it means the second one, then how did the author conclude that all the elements of order p or 4 (if $p=2$) of $L$ are contained in $K$? I like to add that $L/K$ is an abelian p-group of exponent $p$.

My question comes from the this paper.

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The symbol has the same meaning as in other areas of math: I.e. $L$ (as a set) equals the union of the sets $T^g$. Group theory doesn't redefine this notation. – Max Horn Aug 26 '12 at 21:44
@Max: I think some people used the second meaning for that symbole. This link is an example (ams.org/journals/bull/1934-40-12/S0002-9904-1934-05982-2/… ). Please see the second paragraph. – user23954 Aug 26 '12 at 22:51
I mean the third paragraph. – user23954 Aug 26 '12 at 22:54
@unknown(google) could you please write down the question? I could not open the file as it is diverted to a site..... Thanks – Alireza Abdollahi Aug 28 '12 at 15:05
@Alireza Abdollahi: I sent the image to your email. – user23954 Aug 28 '12 at 15:57