How to find number of homomorphisms between z8 and s4?
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How to find number of homomorphisms between z8 and s4?
I check by taking image of generator of z8
Say f:z8---->s4
O(f(1))/8
O(f(1))=1,2,4
S4 has 15 elements of order 2 and 6 elements of order 4
15+6+1(trivial)=22
Is this correct?
finite-groups
asked Nov 15 at 8:43
radhika jain
12
add a comment |
up vote
0
down vote
favorite
How to find number of homomorphisms between z8 and s4?
I check by taking image of generator of z8
Say f:z8---->s4
O(f(1))/8
O(f(1))=1,2,4
S4 has 15 elements of order 2 and 6 elements of order 4
15+6+1(trivial)=22
Is this correct?
finite-groups
asked Nov 15 at 8:43
radhika jain
12
I only count 9 elements of order 2: Six with a single 2-cycle and three with two disjoint 2-cycles. Am I missing something? Regardless of which one of us is counting correctly, the rest of the proof looks good to me.
– Arthur
Nov 15 at 9:02
Arthur, your answer is correct.
– radhika jain
Nov 23 at 17:51
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
How to find number of homomorphisms between z8 and s4?
I check by taking image of generator of z8
Say f:z8---->s4
O(f(1))/8
O(f(1))=1,2,4
S4 has 15 elements of order 2 and 6 elements of order 4
15+6+1(trivial)=22
Is this correct?
finite-groups
asked Nov 15 at 8:43
radhika jain
12
How to find number of homomorphisms between z8 and s4?
I check by taking image of generator of z8
Say f:z8---->s4
O(f(1))/8
O(f(1))=1,2,4
S4 has 15 elements of order 2 and 6 elements of order 4
15+6+1(trivial)=22
Is this correct?
finite-groups
finite-groups
asked Nov 15 at 8:43
radhika jain
12
asked Nov 15 at 8:43
radhika jain
12
asked Nov 15 at 8:43
radhika jain
12
asked Nov 15 at 8:43
radhika jain
12
asked Nov 15 at 8:43
radhika jain
12
12
I only count 9 elements of order 2: Six with a single 2-cycle and three with two disjoint 2-cycles. Am I missing something? Regardless of which one of us is counting correctly, the rest of the proof looks good to me.
– Arthur
Nov 15 at 9:02
Arthur, your answer is correct.
– radhika jain
Nov 23 at 17:51
add a comment |
I only count 9 elements of order 2: Six with a single 2-cycle and three with two disjoint 2-cycles. Am I missing something? Regardless of which one of us is counting correctly, the rest of the proof looks good to me.
– Arthur
Nov 15 at 9:02
Arthur, your answer is correct.
– radhika jain
Nov 23 at 17:51
I only count 9 elements of order 2: Six with a single 2-cycle and three with two disjoint 2-cycles. Am I missing something? Regardless of which one of us is counting correctly, the rest of the proof looks good to me.
– Arthur
Nov 15 at 9:02
I only count 9 elements of order 2: Six with a single 2-cycle and three with two disjoint 2-cycles. Am I missing something? Regardless of which one of us is counting correctly, the rest of the proof looks good to me.
– Arthur
Nov 15 at 9:02
Arthur, your answer is correct.
– radhika jain
Nov 23 at 17:51
Arthur, your answer is correct.
– radhika jain
Nov 23 at 17:51
add a comment |
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I only count 9 elements of order 2: Six with a single 2-cycle and three with two disjoint 2-cycles. Am I missing something? Regardless of which one of us is counting correctly, the rest of the proof looks good to me.
– Arthur
Nov 15 at 9:02
Arthur, your answer is correct.
– radhika jain
Nov 23 at 17:51