Mixing
G1, G2 finite groups such as for all prime p, p-sylow subgroups of G1 isomorpic ($cong$) to p-sylow subgroups of G2 and |G1|=|G2| then G1$cong$G2.
Clash Royale CLAN TAG#URR8PPP
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Decide whether the following staement is true of false. If true, prove it. If false, provide a counterexample
Let G1, G2 be a finite groups such as for all prime p, p-sylow subgroups of G1 isomorpic ($cong$) to p-sylow subgroups of G2 and |G1|=|G2| then G1$cong$G2.
I think this statement is false but I didn't find counterexample yet, I think it's false because I thought about dividing the group to p-sylow subgroups or write her has a direct product of them and then do a uoion or direct product of the isomorphisms but there is no diviton og G1 and G2 to her p-sylow so I couldn't prove it so I tried to find counterexample but I didn't find one.
If you found one please help me :)
finite-groups sylow-theory
asked Jul 27 at 4:56
user579852
305
add a comment |Â
up vote
0
down vote
favorite
Decide whether the following staement is true of false. If true, prove it. If false, provide a counterexample
Let G1, G2 be a finite groups such as for all prime p, p-sylow subgroups of G1 isomorpic ($cong$) to p-sylow subgroups of G2 and |G1|=|G2| then G1$cong$G2.
I think this statement is false but I didn't find counterexample yet, I think it's false because I thought about dividing the group to p-sylow subgroups or write her has a direct product of them and then do a uoion or direct product of the isomorphisms but there is no diviton og G1 and G2 to her p-sylow so I couldn't prove it so I tried to find counterexample but I didn't find one.
If you found one please help me :)
finite-groups sylow-theory
asked Jul 27 at 4:56
user579852
305
It might help (and it would probably go some way to avoiding close votes) if you could articulate why you think the statement is false.
– Brian Tung
Jul 27 at 5:06
thank you I tried to explain I hope it's ok
– user579852
Jul 27 at 5:40
4
Think about groups of order $6$.
– Lord Shark the Unknown
Jul 27 at 6:01
1
Terribly non informative title.
– Did
Jul 27 at 6:18
I thought about what you said but how I can prove that every p-sylow subgroup of $G_1$ isomorpic to p-sylow subgroup of $G_2$??
– user579852
Jul 31 at 11:56
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Decide whether the following staement is true of false. If true, prove it. If false, provide a counterexample
Let G1, G2 be a finite groups such as for all prime p, p-sylow subgroups of G1 isomorpic ($cong$) to p-sylow subgroups of G2 and |G1|=|G2| then G1$cong$G2.
I think this statement is false but I didn't find counterexample yet, I think it's false because I thought about dividing the group to p-sylow subgroups or write her has a direct product of them and then do a uoion or direct product of the isomorphisms but there is no diviton og G1 and G2 to her p-sylow so I couldn't prove it so I tried to find counterexample but I didn't find one.
If you found one please help me :)
finite-groups sylow-theory
asked Jul 27 at 4:56
user579852
305
Decide whether the following staement is true of false. If true, prove it. If false, provide a counterexample
Let G1, G2 be a finite groups such as for all prime p, p-sylow subgroups of G1 isomorpic ($cong$) to p-sylow subgroups of G2 and |G1|=|G2| then G1$cong$G2.
I think this statement is false but I didn't find counterexample yet, I think it's false because I thought about dividing the group to p-sylow subgroups or write her has a direct product of them and then do a uoion or direct product of the isomorphisms but there is no diviton og G1 and G2 to her p-sylow so I couldn't prove it so I tried to find counterexample but I didn't find one.
If you found one please help me :)
finite-groups sylow-theory
asked Jul 27 at 4:56
user579852
305
edited Jul 27 at 9:04
asked Jul 27 at 4:56
user579852
305
asked Jul 27 at 4:56
user579852
305
asked Jul 27 at 4:56
user579852
305
305
It might help (and it would probably go some way to avoiding close votes) if you could articulate why you think the statement is false.
– Brian Tung
Jul 27 at 5:06
thank you I tried to explain I hope it's ok
– user579852
Jul 27 at 5:40
4
Think about groups of order $6$.
– Lord Shark the Unknown
Jul 27 at 6:01
1
Terribly non informative title.
– Did
Jul 27 at 6:18
I thought about what you said but how I can prove that every p-sylow subgroup of $G_1$ isomorpic to p-sylow subgroup of $G_2$??
– user579852
Jul 31 at 11:56
add a comment |Â
It might help (and it would probably go some way to avoiding close votes) if you could articulate why you think the statement is false.
– Brian Tung
Jul 27 at 5:06
thank you I tried to explain I hope it's ok
– user579852
Jul 27 at 5:40
4
Think about groups of order $6$.
– Lord Shark the Unknown
Jul 27 at 6:01
1
Terribly non informative title.
– Did
Jul 27 at 6:18
I thought about what you said but how I can prove that every p-sylow subgroup of $G_1$ isomorpic to p-sylow subgroup of $G_2$??
– user579852
Jul 31 at 11:56
It might help (and it would probably go some way to avoiding close votes) if you could articulate why you think the statement is false.
– Brian Tung
Jul 27 at 5:06
It might help (and it would probably go some way to avoiding close votes) if you could articulate why you think the statement is false.
– Brian Tung
Jul 27 at 5:06
thank you I tried to explain I hope it's ok
– user579852
Jul 27 at 5:40
thank you I tried to explain I hope it's ok
– user579852
Jul 27 at 5:40
4
4
Think about groups of order $6$.
– Lord Shark the Unknown
Jul 27 at 6:01
Think about groups of order $6$.
– Lord Shark the Unknown
Jul 27 at 6:01
1
1
Terribly non informative title.
– Did
Jul 27 at 6:18
Terribly non informative title.
– Did
Jul 27 at 6:18
I thought about what you said but how I can prove that every p-sylow subgroup of $G_1$ isomorpic to p-sylow subgroup of $G_2$??
– user579852
Jul 31 at 11:56
I thought about what you said but how I can prove that every p-sylow subgroup of $G_1$ isomorpic to p-sylow subgroup of $G_2$??
– user579852
Jul 31 at 11:56
add a comment |Â
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It might help (and it would probably go some way to avoiding close votes) if you could articulate why you think the statement is false.
– Brian Tung
Jul 27 at 5:06
thank you I tried to explain I hope it's ok
– user579852
Jul 27 at 5:40
4
Think about groups of order $6$.
– Lord Shark the Unknown
Jul 27 at 6:01
1
Terribly non informative title.
– Did
Jul 27 at 6:18
I thought about what you said but how I can prove that every p-sylow subgroup of $G_1$ isomorpic to p-sylow subgroup of $G_2$??
– user579852
Jul 31 at 11:56