Group of order 275 act on set of size 18, what is the minimum number of orbit of lenght 1?
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Let $G$ be a group of order 275 acting on set of size 18, what is the minimum number of orbit of length 1?
I think it is 2 because we then have $1+1+5+11$ all of the numbers in the sum are divisors of by $275=5^2*11$.
group-theory finite-groups
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Let $G$ be a group of order 275 acting on set of size 18, what is the minimum number of orbit of length 1?
I think it is 2 because we then have $1+1+5+11$ all of the numbers in the sum are divisors of by $275=5^2*11$.
group-theory finite-groups
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Let $G$ be a group of order 275 acting on set of size 18, what is the minimum number of orbit of length 1?
I think it is 2 because we then have $1+1+5+11$ all of the numbers in the sum are divisors of by $275=5^2*11$.
group-theory finite-groups
New contributor
Let $G$ be a group of order 275 acting on set of size 18, what is the minimum number of orbit of length 1?
I think it is 2 because we then have $1+1+5+11$ all of the numbers in the sum are divisors of by $275=5^2*11$.
group-theory finite-groups
group-theory finite-groups
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edited Nov 16 at 10:27
ahulpke
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6,848926
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asked Nov 16 at 10:24
mathnoob
70911
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You have shown that there is a solution which involves 2 orbits of length one, but not yet that you cannot do with fewer.
For that, note that you cannot write $17=18-1$ as a sum of 5s and 11s (clearly no divisor $>18$ will be relevant and 18 cannot be written as a sum of 5s and 11s).
You also need to check that you cannot write 18 as a sum of 5s and 11s.
– C Monsour
Nov 16 at 11:12
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By orbit stabilizer theorem $|G/Stab(a)|=|O(a)|$
With this we know that orbit must divide f order of group So only possibility is 1 . So there are 18 orbits
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2 Answers
2
active
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2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
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up vote
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You have shown that there is a solution which involves 2 orbits of length one, but not yet that you cannot do with fewer.
For that, note that you cannot write $17=18-1$ as a sum of 5s and 11s (clearly no divisor $>18$ will be relevant and 18 cannot be written as a sum of 5s and 11s).
You also need to check that you cannot write 18 as a sum of 5s and 11s.
– C Monsour
Nov 16 at 11:12
add a comment |
up vote
0
down vote
You have shown that there is a solution which involves 2 orbits of length one, but not yet that you cannot do with fewer.
For that, note that you cannot write $17=18-1$ as a sum of 5s and 11s (clearly no divisor $>18$ will be relevant and 18 cannot be written as a sum of 5s and 11s).
You also need to check that you cannot write 18 as a sum of 5s and 11s.
– C Monsour
Nov 16 at 11:12
add a comment |
up vote
0
down vote
up vote
0
down vote
You have shown that there is a solution which involves 2 orbits of length one, but not yet that you cannot do with fewer.
For that, note that you cannot write $17=18-1$ as a sum of 5s and 11s (clearly no divisor $>18$ will be relevant and 18 cannot be written as a sum of 5s and 11s).
You have shown that there is a solution which involves 2 orbits of length one, but not yet that you cannot do with fewer.
For that, note that you cannot write $17=18-1$ as a sum of 5s and 11s (clearly no divisor $>18$ will be relevant and 18 cannot be written as a sum of 5s and 11s).
edited Nov 16 at 14:23
answered Nov 16 at 10:29
ahulpke
6,848926
6,848926
You also need to check that you cannot write 18 as a sum of 5s and 11s.
– C Monsour
Nov 16 at 11:12
add a comment |
You also need to check that you cannot write 18 as a sum of 5s and 11s.
– C Monsour
Nov 16 at 11:12
You also need to check that you cannot write 18 as a sum of 5s and 11s.
– C Monsour
Nov 16 at 11:12
You also need to check that you cannot write 18 as a sum of 5s and 11s.
– C Monsour
Nov 16 at 11:12
add a comment |
up vote
0
down vote
By orbit stabilizer theorem $|G/Stab(a)|=|O(a)|$
With this we know that orbit must divide f order of group So only possibility is 1 . So there are 18 orbits
add a comment |
up vote
0
down vote
By orbit stabilizer theorem $|G/Stab(a)|=|O(a)|$
With this we know that orbit must divide f order of group So only possibility is 1 . So there are 18 orbits
add a comment |
up vote
0
down vote
up vote
0
down vote
By orbit stabilizer theorem $|G/Stab(a)|=|O(a)|$
With this we know that orbit must divide f order of group So only possibility is 1 . So there are 18 orbits
By orbit stabilizer theorem $|G/Stab(a)|=|O(a)|$
With this we know that orbit must divide f order of group So only possibility is 1 . So there are 18 orbits
answered Nov 16 at 14:56
Shubham
1,2951518
1,2951518
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