Recent content by moont14263

This question has been answered in this link http://math.stackexchange.com/questions/1720619/sylow-subgroup-of-some-factor-group

Hi. I have the following question: Let G be a finite group. Let K be a subgroup of G and let N be a normal subgroup of G. Let P be a Sylow p-subgroup of K. Is PN/N is a Sylow p-subgroup of KN/N? Here is what I think. Since PN/N \cong P/(P \cap N), then PN/N is a p-subgroup of KN/N. Now...

In case PQ is a subgroup of G, then PQ=QP.

Homework Statement I am trying to prove the following: Let G be a finite group and let \{p,q\} be the set of primes dividing the order of G. Show that PQ=QP for any P Sylow p-subgroup of G and Q Sylow q-subgroup of G. Deduce that G=PQ. Homework Equations The set PQ=\{xy: x \in P \text{ and }...

Notice that |HK|=\frac{|H||K|}{|H\cap K|}, for any subgroups H and K of G. Sorry, I could not add it there, but thank you very much.

Let G be a finite group. Suppose that every element of order 2 of G has a complement in G, then G has no element of order 4. Proof. Let x be an element of G of order 4. By hypothesis, G=<x^{2}> K and < x^{2}> \capK=1 for some subgroup K of G. Clearly, G=< x> K and < x>\cap K=1$, but |G|=|<...

The symbol L=\bigcup_{g \in G} T^{g}, does it mean the union of sets or L=<T^{g},g \in G>and, if it the union of sets, then how did he gets that L equals to that union?

My question is about the shaded area in the attachment? How did the author get that all the elements of order p or 4 of L are contained in K? I mentioned the abstract but I do not think there is a need for that. Help?

Excuse me, how did you know that m is less than the exponent of G/Hi?

thank you very much.

Let p be a prime. Let H_{i}, i=1,...,n be normal subgroups of a finite group G. I want to prove the following: If G/H_{i}, i=1,...,n are abelian groups of exponent dividing p-1, then G/N is abelian group of exponent dividing p-1 where N=\bigcap H_{i} ,i=1,...,n. Proof: Since G/H_{i}...

I contacted one of the authors and he told me that there was a mistake. He just altered his definition to make things work. I do not know if there are more things that need to be fixed. I just wrote this comment to let you know. Thank you very much for every one specially DonAntonio. As you...

Thanks for the advice. I'll send them an email.

I want to prove Lemma 2.1(1) in this paper, the first pdf file in the page This is my proof. . Since H is X−s−permutable in G, then for P Sylow of G there exists x \in X such that P^{x}H=HP^{x}. The Sylow of N are of the form P∩N. Thus,(P∩N)^{x}H=H(P∩N)^{x}. Hence, H is X−s−permutable in N...

Here is an example of what I am talking about. I made up this theorem. Let H be a normal subgroup of a finite group G. If all Sylow p-subgroup P of G are conjugate in H then G is solvable. Conjugate in H means the set {P^{h}:h \in H} contain all Sylow p-subgroup of G where P is a...