(Permutations) For $n ≥ 2$,there are at least n subgroups of Sn of order $(n − 1)!$
1
For $n ≥ 2$, show that there are at least n subgroups of Sn of order $(n − 1)!$
permutations permutation-cycles
edited Nov 26 at 18:34
Key Flex
7,46941232
asked Nov 26 at 18:32
awkwardturtle
61
add a comment |
1
For $n ≥ 2$, show that there are at least n subgroups of Sn of order $(n − 1)!$
permutations permutation-cycles
edited Nov 26 at 18:34
Key Flex
7,46941232
asked Nov 26 at 18:32
awkwardturtle
61
Can you embed $S_{n-1}$ into $S_n$ in at least $n$ different ways?
– Dzoooks
Nov 26 at 18:46
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 22 at 0:08
add a comment |
1
1
1
For $n ≥ 2$, show that there are at least n subgroups of Sn of order $(n − 1)!$
permutations permutation-cycles
edited Nov 26 at 18:34
Key Flex
7,46941232
asked Nov 26 at 18:32
awkwardturtle
61
For $n ≥ 2$, show that there are at least n subgroups of Sn of order $(n − 1)!$
permutations permutation-cycles
permutations permutation-cycles
edited Nov 26 at 18:34
Key Flex
7,46941232
asked Nov 26 at 18:32
awkwardturtle
61
edited Nov 26 at 18:34
Key Flex
7,46941232
asked Nov 26 at 18:32
awkwardturtle
61
edited Nov 26 at 18:34
Key Flex
7,46941232
edited Nov 26 at 18:34
Key Flex
7,46941232
edited Nov 26 at 18:34
Key Flex
7,46941232
7,46941232
asked Nov 26 at 18:32
awkwardturtle
61
asked Nov 26 at 18:32
awkwardturtle
61
asked Nov 26 at 18:32
awkwardturtle
61
61
Can you embed $S_{n-1}$ into $S_n$ in at least $n$ different ways?
– Dzoooks
Nov 26 at 18:46
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 22 at 0:08
add a comment |
Can you embed $S_{n-1}$ into $S_n$ in at least $n$ different ways?
– Dzoooks
Nov 26 at 18:46
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 22 at 0:08
Can you embed $S_{n-1}$ into $S_n$ in at least $n$ different ways?
– Dzoooks
Nov 26 at 18:46
Can you embed $S_{n-1}$ into $S_n$ in at least $n$ different ways?
– Dzoooks
Nov 26 at 18:46
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 22 at 0:08
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 22 at 0:08
add a comment |
1 Answer
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For $k in {1,..,n}$, let
$$H_k={ sigma in S_n | sigma(k)=k }$$
Then the subsets $H_1, .. H_n$ are subgroups of order $(n-1)!$ that are mutually distinct (I leave that to you to check).
answered Nov 26 at 18:41
M. Van
2,555311
add a comment |
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For $k in {1,..,n}$, let
$$H_k={ sigma in S_n | sigma(k)=k }$$
Then the subsets $H_1, .. H_n$ are subgroups of order $(n-1)!$ that are mutually distinct (I leave that to you to check).
answered Nov 26 at 18:41
M. Van
2,555311
add a comment |
0
For $k in {1,..,n}$, let
$$H_k={ sigma in S_n | sigma(k)=k }$$
Then the subsets $H_1, .. H_n$ are subgroups of order $(n-1)!$ that are mutually distinct (I leave that to you to check).
answered Nov 26 at 18:41
M. Van
2,555311
add a comment |
0
0
0
For $k in {1,..,n}$, let
$$H_k={ sigma in S_n | sigma(k)=k }$$
Then the subsets $H_1, .. H_n$ are subgroups of order $(n-1)!$ that are mutually distinct (I leave that to you to check).
answered Nov 26 at 18:41
M. Van
2,555311
For $k in {1,..,n}$, let
$$H_k={ sigma in S_n | sigma(k)=k }$$
Then the subsets $H_1, .. H_n$ are subgroups of order $(n-1)!$ that are mutually distinct (I leave that to you to check).
answered Nov 26 at 18:41
M. Van
2,555311
answered Nov 26 at 18:41
M. Van
2,555311
answered Nov 26 at 18:41
M. Van
2,555311
answered Nov 26 at 18:41
M. Van
2,555311
2,555311
add a comment |
add a comment |
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Can you embed $S_{n-1}$ into $S_n$ in at least $n$ different ways?
– Dzoooks
Nov 26 at 18:46
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 22 at 0:08