Mixing
Minimum number of subgroup whose union is $ mathbb z_4 times mathbb z_4$ .
$begingroup$
Consider the group $ mathbb z_4 times mathbb z_4$ of order 16 under component wise addition modulo 4. if G is union of $n$ subgroup of order 4 then minimum value of n is
a) 7
b) 4
c) 5
d) 6
My attempt:
number of elements of order 4 is 12 .these elements should be in subgroup, so minimum number of subgroup implies optimal way of putting these elements.but maximum number of element 4 in a group of order 4 is 2. hence we divide by 2 .and we get 6.
but i'm not satisfy with my answer and i feel something is wrong . is this correct ? if not, please help !
group-theory finite-groups direct-product
asked Jan 27 at 11:22
Cloud JRCloud JR
915518
$endgroup$
add a comment |
$begingroup$
Consider the group $ mathbb z_4 times mathbb z_4$ of order 16 under component wise addition modulo 4. if G is union of $n$ subgroup of order 4 then minimum value of n is
a) 7
b) 4
c) 5
d) 6
My attempt:
number of elements of order 4 is 12 .these elements should be in subgroup, so minimum number of subgroup implies optimal way of putting these elements.but maximum number of element 4 in a group of order 4 is 2. hence we divide by 2 .and we get 6.
but i'm not satisfy with my answer and i feel something is wrong . is this correct ? if not, please help !
group-theory finite-groups direct-product
asked Jan 27 at 11:22
Cloud JRCloud JR
915518
$endgroup$
$begingroup$
You've proved $6$ is a lower bound. Now see whether you can find six subgroups that work.
$endgroup$
– Gerry Myerson
Jan 27 at 12:00
$begingroup$
Making any progress?
$endgroup$
– Gerry Myerson
Jan 29 at 8:26
1
$begingroup$
@GerryMyerson first if all thank you for remember me on your busy day ..i actually found 6 subgroup which has all elements of G . And also i complete my argument .Thank a lot..
$endgroup$
– Cloud JR
Jan 29 at 14:53
$begingroup$
Let me encourage you to post your findings as an answer to your question.
$endgroup$
– Gerry Myerson
Jan 29 at 20:42
1
$begingroup$
Its 2 am here.... I will post it tomorrow...plz forgive me
$endgroup$
– Cloud JR
Jan 29 at 20:55
add a comment |
$begingroup$
Consider the group $ mathbb z_4 times mathbb z_4$ of order 16 under component wise addition modulo 4. if G is union of $n$ subgroup of order 4 then minimum value of n is
a) 7
b) 4
c) 5
d) 6
My attempt:
number of elements of order 4 is 12 .these elements should be in subgroup, so minimum number of subgroup implies optimal way of putting these elements.but maximum number of element 4 in a group of order 4 is 2. hence we divide by 2 .and we get 6.
but i'm not satisfy with my answer and i feel something is wrong . is this correct ? if not, please help !
group-theory finite-groups direct-product
asked Jan 27 at 11:22
Cloud JRCloud JR
915518
$endgroup$
Consider the group $ mathbb z_4 times mathbb z_4$ of order 16 under component wise addition modulo 4. if G is union of $n$ subgroup of order 4 then minimum value of n is
a) 7
b) 4
c) 5
d) 6
My attempt:
number of elements of order 4 is 12 .these elements should be in subgroup, so minimum number of subgroup implies optimal way of putting these elements.but maximum number of element 4 in a group of order 4 is 2. hence we divide by 2 .and we get 6.
but i'm not satisfy with my answer and i feel something is wrong . is this correct ? if not, please help !
group-theory finite-groups direct-product
group-theory finite-groups direct-product
asked Jan 27 at 11:22
Cloud JRCloud JR
915518
asked Jan 27 at 11:22
Cloud JRCloud JR
915518
asked Jan 27 at 11:22
Cloud JRCloud JR
915518
asked Jan 27 at 11:22
Cloud JRCloud JR
915518
asked Jan 27 at 11:22
Cloud JRCloud JR
915518
915518
$begingroup$
You've proved $6$ is a lower bound. Now see whether you can find six subgroups that work.
$endgroup$
– Gerry Myerson
Jan 27 at 12:00
$begingroup$
Making any progress?
$endgroup$
– Gerry Myerson
Jan 29 at 8:26
1
$begingroup$
@GerryMyerson first if all thank you for remember me on your busy day ..i actually found 6 subgroup which has all elements of G . And also i complete my argument .Thank a lot..
$endgroup$
– Cloud JR
Jan 29 at 14:53
$begingroup$
Let me encourage you to post your findings as an answer to your question.
$endgroup$
– Gerry Myerson
Jan 29 at 20:42
1
$begingroup$
Its 2 am here.... I will post it tomorrow...plz forgive me
$endgroup$
– Cloud JR
Jan 29 at 20:55
add a comment |
$begingroup$
You've proved $6$ is a lower bound. Now see whether you can find six subgroups that work.
$endgroup$
– Gerry Myerson
Jan 27 at 12:00
$begingroup$
Making any progress?
$endgroup$
– Gerry Myerson
Jan 29 at 8:26
1
$begingroup$
@GerryMyerson first if all thank you for remember me on your busy day ..i actually found 6 subgroup which has all elements of G . And also i complete my argument .Thank a lot..
$endgroup$
– Cloud JR
Jan 29 at 14:53
$begingroup$
Let me encourage you to post your findings as an answer to your question.
$endgroup$
– Gerry Myerson
Jan 29 at 20:42
1
$begingroup$
Its 2 am here.... I will post it tomorrow...plz forgive me
$endgroup$
– Cloud JR
Jan 29 at 20:55
$begingroup$
You've proved $6$ is a lower bound. Now see whether you can find six subgroups that work.
$endgroup$
– Gerry Myerson
Jan 27 at 12:00
$begingroup$
You've proved $6$ is a lower bound. Now see whether you can find six subgroups that work.
$endgroup$
– Gerry Myerson
Jan 27 at 12:00
$begingroup$
Making any progress?
$endgroup$
– Gerry Myerson
Jan 29 at 8:26
$begingroup$
Making any progress?
$endgroup$
– Gerry Myerson
Jan 29 at 8:26
1
1
$begingroup$
@GerryMyerson first if all thank you for remember me on your busy day ..i actually found 6 subgroup which has all elements of G . And also i complete my argument .Thank a lot..
$endgroup$
– Cloud JR
Jan 29 at 14:53
$begingroup$
@GerryMyerson first if all thank you for remember me on your busy day ..i actually found 6 subgroup which has all elements of G . And also i complete my argument .Thank a lot..
$endgroup$
– Cloud JR
Jan 29 at 14:53
$begingroup$
Let me encourage you to post your findings as an answer to your question.
$endgroup$
– Gerry Myerson
Jan 29 at 20:42
$begingroup$
Let me encourage you to post your findings as an answer to your question.
$endgroup$
– Gerry Myerson
Jan 29 at 20:42
1
1
$begingroup$
Its 2 am here.... I will post it tomorrow...plz forgive me
$endgroup$
– Cloud JR
Jan 29 at 20:55
$begingroup$
Its 2 am here.... I will post it tomorrow...plz forgive me
$endgroup$
– Cloud JR
Jan 29 at 20:55
add a comment |
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$begingroup$
You've proved $6$ is a lower bound. Now see whether you can find six subgroups that work.
$endgroup$
– Gerry Myerson
Jan 27 at 12:00
$begingroup$
Making any progress?
$endgroup$
– Gerry Myerson
Jan 29 at 8:26
1
$begingroup$
@GerryMyerson first if all thank you for remember me on your busy day ..i actually found 6 subgroup which has all elements of G . And also i complete my argument .Thank a lot..
$endgroup$
– Cloud JR
Jan 29 at 14:53
$begingroup$
Let me encourage you to post your findings as an answer to your question.
$endgroup$
– Gerry Myerson
Jan 29 at 20:42
1
$begingroup$
Its 2 am here.... I will post it tomorrow...plz forgive me
$endgroup$
– Cloud JR
Jan 29 at 20:55