Mixing
What is the largest subgroup of Z contained in 10Z and 2Z?
$begingroup$
I know this is really easy but I can't find anything to confirm my answer in any notes and the fact this is 4 marks throws me off.
Is it simply just 2Z? As 10Z is just the integers that are multiples of 10 and 14Z multiples of 14?
group-theory
asked Jan 9 at 15:31
AnoUser1AnoUser1
735
$endgroup$
add a comment |
$begingroup$
I know this is really easy but I can't find anything to confirm my answer in any notes and the fact this is 4 marks throws me off.
Is it simply just 2Z? As 10Z is just the integers that are multiples of 10 and 14Z multiples of 14?
group-theory
asked Jan 9 at 15:31
AnoUser1AnoUser1
735
$endgroup$
$begingroup$
Is 2Z contained in 10Z?
$endgroup$
– Wojowu
Jan 9 at 15:34
$begingroup$
right, read it again and i have to find the LCM then?
$endgroup$
– AnoUser1
Jan 9 at 15:37
$begingroup$
@AnoUser1 that's right
$endgroup$
– Omnomnomnom
Jan 9 at 15:40
add a comment |
$begingroup$
I know this is really easy but I can't find anything to confirm my answer in any notes and the fact this is 4 marks throws me off.
Is it simply just 2Z? As 10Z is just the integers that are multiples of 10 and 14Z multiples of 14?
group-theory
asked Jan 9 at 15:31
AnoUser1AnoUser1
735
$endgroup$
I know this is really easy but I can't find anything to confirm my answer in any notes and the fact this is 4 marks throws me off.
Is it simply just 2Z? As 10Z is just the integers that are multiples of 10 and 14Z multiples of 14?
group-theory
group-theory
asked Jan 9 at 15:31
AnoUser1AnoUser1
735
asked Jan 9 at 15:31
AnoUser1AnoUser1
735
asked Jan 9 at 15:31
AnoUser1AnoUser1
735
asked Jan 9 at 15:31
AnoUser1AnoUser1
735
asked Jan 9 at 15:31
AnoUser1AnoUser1
735
735
$begingroup$
Is 2Z contained in 10Z?
$endgroup$
– Wojowu
Jan 9 at 15:34
$begingroup$
right, read it again and i have to find the LCM then?
$endgroup$
– AnoUser1
Jan 9 at 15:37
$begingroup$
@AnoUser1 that's right
$endgroup$
– Omnomnomnom
Jan 9 at 15:40
add a comment |
$begingroup$
Is 2Z contained in 10Z?
$endgroup$
– Wojowu
Jan 9 at 15:34
$begingroup$
right, read it again and i have to find the LCM then?
$endgroup$
– AnoUser1
Jan 9 at 15:37
$begingroup$
@AnoUser1 that's right
$endgroup$
– Omnomnomnom
Jan 9 at 15:40
$begingroup$
Is 2Z contained in 10Z?
$endgroup$
– Wojowu
Jan 9 at 15:34
$begingroup$
Is 2Z contained in 10Z?
$endgroup$
– Wojowu
Jan 9 at 15:34
$begingroup$
right, read it again and i have to find the LCM then?
$endgroup$
– AnoUser1
Jan 9 at 15:37
$begingroup$
right, read it again and i have to find the LCM then?
$endgroup$
– AnoUser1
Jan 9 at 15:37
$begingroup$
@AnoUser1 that's right
$endgroup$
– Omnomnomnom
Jan 9 at 15:40
$begingroup$
@AnoUser1 that's right
$endgroup$
– Omnomnomnom
Jan 9 at 15:40
add a comment |
1 Answer
1
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$begingroup$
The other way around: $10Bbb Zsubset 2Bbb Z$.
In general it would be $operatorname{lcm}(m,n)Bbb Z$ is the largest subgroup of $mBbb Z$ and $nBbb Z$.
answered Jan 9 at 15:41
Chris CusterChris Custer
12.5k3825
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
The other way around: $10Bbb Zsubset 2Bbb Z$.
In general it would be $operatorname{lcm}(m,n)Bbb Z$ is the largest subgroup of $mBbb Z$ and $nBbb Z$.
answered Jan 9 at 15:41
Chris CusterChris Custer
12.5k3825
$endgroup$
add a comment |
$begingroup$
The other way around: $10Bbb Zsubset 2Bbb Z$.
In general it would be $operatorname{lcm}(m,n)Bbb Z$ is the largest subgroup of $mBbb Z$ and $nBbb Z$.
answered Jan 9 at 15:41
Chris CusterChris Custer
12.5k3825
$endgroup$
add a comment |
$begingroup$
The other way around: $10Bbb Zsubset 2Bbb Z$.
In general it would be $operatorname{lcm}(m,n)Bbb Z$ is the largest subgroup of $mBbb Z$ and $nBbb Z$.
answered Jan 9 at 15:41
Chris CusterChris Custer
12.5k3825
$endgroup$
The other way around: $10Bbb Zsubset 2Bbb Z$.
In general it would be $operatorname{lcm}(m,n)Bbb Z$ is the largest subgroup of $mBbb Z$ and $nBbb Z$.
answered Jan 9 at 15:41
Chris CusterChris Custer
12.5k3825
answered Jan 9 at 15:41
Chris CusterChris Custer
12.5k3825
answered Jan 9 at 15:41
Chris CusterChris Custer
12.5k3825
answered Jan 9 at 15:41
Chris CusterChris Custer
12.5k3825
12.5k3825
add a comment |
add a comment |
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$begingroup$
Is 2Z contained in 10Z?
$endgroup$
– Wojowu
Jan 9 at 15:34
$begingroup$
right, read it again and i have to find the LCM then?
$endgroup$
– AnoUser1
Jan 9 at 15:37
$begingroup$
@AnoUser1 that's right
$endgroup$
– Omnomnomnom
Jan 9 at 15:40