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Let G be a finite group and N$lhd$G such as p||N| (p dividing the order of N). Then for all P p-sylow subgroup of G, N$cap$P$nee$
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Decide whether the following staement is true of false If true, prove it. If false, provide a counterexample
Let G be a finite group and N$lhd$G such as p||N| (p dividing the order of N). Then for all P p-sylow subgroup of G, N$cap$P$nee$
I think it's false but I don't know how to prove it..
please help :)
finite-groups sylow-theory
asked Jul 27 at 5:47
user579852
305
add a comment |Â
up vote
-3
down vote
favorite
Decide whether the following staement is true of false If true, prove it. If false, provide a counterexample
Let G be a finite group and N$lhd$G such as p||N| (p dividing the order of N). Then for all P p-sylow subgroup of G, N$cap$P$nee$
I think it's false but I don't know how to prove it..
please help :)
finite-groups sylow-theory
asked Jul 27 at 5:47
user579852
305
2
You really need to stop using the same title for all of your questions.
– Tobias Kildetoft
Jul 27 at 5:50
Consider the image of $P$ under the projection map $Gto G/N$.
– Lord Shark the Unknown
Jul 27 at 5:55
The sentence "I think it's false but I don't know how to prove it.. please help :)" is your only contribution to this. Sorry but this is not enough. VTC.
– Did
Jul 27 at 6:30
I wrote this here because I need help not because I already found an example, I tried to found one before I wrote this here but the one I thought about didn't match every part of the question. You don't have to help me it's your decision but I'd be happy to get help from others that can and want to help
– user579852
Jul 27 at 6:35
add a comment |Â
up vote
-3
down vote
favorite
up vote
-3
down vote
favorite
Decide whether the following staement is true of false If true, prove it. If false, provide a counterexample
Let G be a finite group and N$lhd$G such as p||N| (p dividing the order of N). Then for all P p-sylow subgroup of G, N$cap$P$nee$
I think it's false but I don't know how to prove it..
please help :)
finite-groups sylow-theory
asked Jul 27 at 5:47
user579852
305
Decide whether the following staement is true of false If true, prove it. If false, provide a counterexample
Let G be a finite group and N$lhd$G such as p||N| (p dividing the order of N). Then for all P p-sylow subgroup of G, N$cap$P$nee$
I think it's false but I don't know how to prove it..
please help :)
finite-groups sylow-theory
asked Jul 27 at 5:47
user579852
305
edited Jul 27 at 8:54
asked Jul 27 at 5:47
user579852
305
asked Jul 27 at 5:47
user579852
305
asked Jul 27 at 5:47
user579852
305
305
2
You really need to stop using the same title for all of your questions.
– Tobias Kildetoft
Jul 27 at 5:50
Consider the image of $P$ under the projection map $Gto G/N$.
– Lord Shark the Unknown
Jul 27 at 5:55
The sentence "I think it's false but I don't know how to prove it.. please help :)" is your only contribution to this. Sorry but this is not enough. VTC.
– Did
Jul 27 at 6:30
I wrote this here because I need help not because I already found an example, I tried to found one before I wrote this here but the one I thought about didn't match every part of the question. You don't have to help me it's your decision but I'd be happy to get help from others that can and want to help
– user579852
Jul 27 at 6:35
add a comment |Â
2
You really need to stop using the same title for all of your questions.
– Tobias Kildetoft
Jul 27 at 5:50
Consider the image of $P$ under the projection map $Gto G/N$.
– Lord Shark the Unknown
Jul 27 at 5:55
The sentence "I think it's false but I don't know how to prove it.. please help :)" is your only contribution to this. Sorry but this is not enough. VTC.
– Did
Jul 27 at 6:30
I wrote this here because I need help not because I already found an example, I tried to found one before I wrote this here but the one I thought about didn't match every part of the question. You don't have to help me it's your decision but I'd be happy to get help from others that can and want to help
– user579852
Jul 27 at 6:35
2
2
You really need to stop using the same title for all of your questions.
– Tobias Kildetoft
Jul 27 at 5:50
You really need to stop using the same title for all of your questions.
– Tobias Kildetoft
Jul 27 at 5:50
Consider the image of $P$ under the projection map $Gto G/N$.
– Lord Shark the Unknown
Jul 27 at 5:55
Consider the image of $P$ under the projection map $Gto G/N$.
– Lord Shark the Unknown
Jul 27 at 5:55
The sentence "I think it's false but I don't know how to prove it.. please help :)" is your only contribution to this. Sorry but this is not enough. VTC.
– Did
Jul 27 at 6:30
The sentence "I think it's false but I don't know how to prove it.. please help :)" is your only contribution to this. Sorry but this is not enough. VTC.
– Did
Jul 27 at 6:30
I wrote this here because I need help not because I already found an example, I tried to found one before I wrote this here but the one I thought about didn't match every part of the question. You don't have to help me it's your decision but I'd be happy to get help from others that can and want to help
– user579852
Jul 27 at 6:35
I wrote this here because I need help not because I already found an example, I tried to found one before I wrote this here but the one I thought about didn't match every part of the question. You don't have to help me it's your decision but I'd be happy to get help from others that can and want to help
– user579852
Jul 27 at 6:35
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
0
down vote
Let $p, q$ be distinct prime numbers. Consider $mathbbZ/pmathbbZtimesmathbbZ/qmathbbZ$, $N=mathbbZ/pmathbbZtimes0$ and $P=0timesmathbbZ/qmathbbZ$.
answered Jul 27 at 5:58
Tsemo Aristide
50.9k11143
Your $P$ is not a $p$-Sylow subgroup.
– Lord Shark the Unknown
Jul 27 at 10:36
how do I prove that N is normal and that P is p-sylow? and what is the order of N? does p dividing this order?
– user579852
Jul 31 at 11:59
@Tsemo Aristide hi can you explain to me why $Nlhd G$?
– user579852
Aug 4 at 6:42
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Let $p, q$ be distinct prime numbers. Consider $mathbbZ/pmathbbZtimesmathbbZ/qmathbbZ$, $N=mathbbZ/pmathbbZtimes0$ and $P=0timesmathbbZ/qmathbbZ$.
answered Jul 27 at 5:58
Tsemo Aristide
50.9k11143
Your $P$ is not a $p$-Sylow subgroup.
– Lord Shark the Unknown
Jul 27 at 10:36
how do I prove that N is normal and that P is p-sylow? and what is the order of N? does p dividing this order?
– user579852
Jul 31 at 11:59
@Tsemo Aristide hi can you explain to me why $Nlhd G$?
– user579852
Aug 4 at 6:42
add a comment |Â
up vote
0
down vote
Let $p, q$ be distinct prime numbers. Consider $mathbbZ/pmathbbZtimesmathbbZ/qmathbbZ$, $N=mathbbZ/pmathbbZtimes0$ and $P=0timesmathbbZ/qmathbbZ$.
answered Jul 27 at 5:58
Tsemo Aristide
50.9k11143
Your $P$ is not a $p$-Sylow subgroup.
– Lord Shark the Unknown
Jul 27 at 10:36
how do I prove that N is normal and that P is p-sylow? and what is the order of N? does p dividing this order?
– user579852
Jul 31 at 11:59
@Tsemo Aristide hi can you explain to me why $Nlhd G$?
– user579852
Aug 4 at 6:42
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Let $p, q$ be distinct prime numbers. Consider $mathbbZ/pmathbbZtimesmathbbZ/qmathbbZ$, $N=mathbbZ/pmathbbZtimes0$ and $P=0timesmathbbZ/qmathbbZ$.
answered Jul 27 at 5:58
Tsemo Aristide
50.9k11143
Let $p, q$ be distinct prime numbers. Consider $mathbbZ/pmathbbZtimesmathbbZ/qmathbbZ$, $N=mathbbZ/pmathbbZtimes0$ and $P=0timesmathbbZ/qmathbbZ$.
answered Jul 27 at 5:58
Tsemo Aristide
50.9k11143
edited Jul 27 at 6:32
answered Jul 27 at 5:58
Tsemo Aristide
50.9k11143
answered Jul 27 at 5:58
Tsemo Aristide
50.9k11143
answered Jul 27 at 5:58
Tsemo Aristide
50.9k11143
50.9k11143
Your $P$ is not a $p$-Sylow subgroup.
– Lord Shark the Unknown
Jul 27 at 10:36
how do I prove that N is normal and that P is p-sylow? and what is the order of N? does p dividing this order?
– user579852
Jul 31 at 11:59
@Tsemo Aristide hi can you explain to me why $Nlhd G$?
– user579852
Aug 4 at 6:42
add a comment |Â
Your $P$ is not a $p$-Sylow subgroup.
– Lord Shark the Unknown
Jul 27 at 10:36
how do I prove that N is normal and that P is p-sylow? and what is the order of N? does p dividing this order?
– user579852
Jul 31 at 11:59
@Tsemo Aristide hi can you explain to me why $Nlhd G$?
– user579852
Aug 4 at 6:42
Your $P$ is not a $p$-Sylow subgroup.
– Lord Shark the Unknown
Jul 27 at 10:36
Your $P$ is not a $p$-Sylow subgroup.
– Lord Shark the Unknown
Jul 27 at 10:36
how do I prove that N is normal and that P is p-sylow? and what is the order of N? does p dividing this order?
– user579852
Jul 31 at 11:59
how do I prove that N is normal and that P is p-sylow? and what is the order of N? does p dividing this order?
– user579852
Jul 31 at 11:59
@Tsemo Aristide hi can you explain to me why $Nlhd G$?
– user579852
Aug 4 at 6:42
@Tsemo Aristide hi can you explain to me why $Nlhd G$?
– user579852
Aug 4 at 6:42
add a comment |Â
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2
You really need to stop using the same title for all of your questions.
– Tobias Kildetoft
Jul 27 at 5:50
Consider the image of $P$ under the projection map $Gto G/N$.
– Lord Shark the Unknown
Jul 27 at 5:55
The sentence "I think it's false but I don't know how to prove it.. please help :)" is your only contribution to this. Sorry but this is not enough. VTC.
– Did
Jul 27 at 6:30
I wrote this here because I need help not because I already found an example, I tried to found one before I wrote this here but the one I thought about didn't match every part of the question. You don't have to help me it's your decision but I'd be happy to get help from others that can and want to help
– user579852
Jul 27 at 6:35