Let $(G, cdot)$ be a finite group, $H < G$ (proper subgroup), and $x in H$ such that $C_{H}(x) <...
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I have a problem where I am given these two facts, but I do not seem to be able to hit upon relevant consequences of them. The one I could figure it out is the most obvious one:
$C_{H}(x) = H cap C_{G}(x)$, so there exists $g in G$, such that $g in C_{G}(x)$ but $g notin H$
What other relevant consequences are this? Please simply state them without giving me a proof, since I would like to prove them myself.
group-theory finite-groups
asked Dec 1 at 20:22
user89
6711647
put on hold as unclear what you're asking by Arturo Magidin, Brahadeesh, user10354138, KReiser, Chinnapparaj R Dec 2 at 9:29
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
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I have a problem where I am given these two facts, but I do not seem to be able to hit upon relevant consequences of them. The one I could figure it out is the most obvious one:
$C_{H}(x) = H cap C_{G}(x)$, so there exists $g in G$, such that $g in C_{G}(x)$ but $g notin H$
What other relevant consequences are this? Please simply state them without giving me a proof, since I would like to prove them myself.
group-theory finite-groups
asked Dec 1 at 20:22
user89
6711647
put on hold as unclear what you're asking by Arturo Magidin, Brahadeesh, user10354138, KReiser, Chinnapparaj R Dec 2 at 9:29
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
"Relevant" really depends on what you want to do with the statement, doesn't it? What conclusions are you trying to draw?
– Arturo Magidin
Dec 2 at 0:01
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have a problem where I am given these two facts, but I do not seem to be able to hit upon relevant consequences of them. The one I could figure it out is the most obvious one:
$C_{H}(x) = H cap C_{G}(x)$, so there exists $g in G$, such that $g in C_{G}(x)$ but $g notin H$
What other relevant consequences are this? Please simply state them without giving me a proof, since I would like to prove them myself.
group-theory finite-groups
asked Dec 1 at 20:22
user89
6711647
I have a problem where I am given these two facts, but I do not seem to be able to hit upon relevant consequences of them. The one I could figure it out is the most obvious one:
$C_{H}(x) = H cap C_{G}(x)$, so there exists $g in G$, such that $g in C_{G}(x)$ but $g notin H$
What other relevant consequences are this? Please simply state them without giving me a proof, since I would like to prove them myself.
group-theory finite-groups
group-theory finite-groups
asked Dec 1 at 20:22
user89
6711647
asked Dec 1 at 20:22
user89
6711647
asked Dec 1 at 20:22
user89
6711647
asked Dec 1 at 20:22
user89
6711647
asked Dec 1 at 20:22
user89
6711647
6711647
put on hold as unclear what you're asking by Arturo Magidin, Brahadeesh, user10354138, KReiser, Chinnapparaj R Dec 2 at 9:29
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as unclear what you're asking by Arturo Magidin, Brahadeesh, user10354138, KReiser, Chinnapparaj R Dec 2 at 9:29
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
"Relevant" really depends on what you want to do with the statement, doesn't it? What conclusions are you trying to draw?
– Arturo Magidin
Dec 2 at 0:01
add a comment |
1
"Relevant" really depends on what you want to do with the statement, doesn't it? What conclusions are you trying to draw?
– Arturo Magidin
Dec 2 at 0:01
1
1
"Relevant" really depends on what you want to do with the statement, doesn't it? What conclusions are you trying to draw?
– Arturo Magidin
Dec 2 at 0:01
"Relevant" really depends on what you want to do with the statement, doesn't it? What conclusions are you trying to draw?
– Arturo Magidin
Dec 2 at 0:01
add a comment |
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1
"Relevant" really depends on what you want to do with the statement, doesn't it? What conclusions are you trying to draw?
– Arturo Magidin
Dec 2 at 0:01