Are there any other subgroups of order 3 & 2 ? For his vere'll consider all subsets of 3 and 2 elememts of S3 and use equations af-f'z and $3 gf ² - fg to check if they are subgroups 2 5=[ e, f, f, g, fg, f²g]
Are there any other subgroups of order 3 & 2 ? For his vere'll consider all subsets of 3 and 2 elememts of S3 and use equations af-f'z and $3 gf ² - fg to check if they are subgroups 2 5=[ e, f, f, g, fg, f²g]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Are there any
other subgroups of
=
order 3 & 2 ? For his vere'll consider
all subsets of 3 and 2 elements
of $3 and use equations of fiz and
gf² = fg to check if they are subgroups
5-{e, f, f²g, fg, f²g]
}
All Subsets of 3 elements
{ e. f₁ f²} = < f> = < f ² >
{e₁
he₁ f₁ g y = Not a Subgp. Since £g¢{ }
2
17
{e, f, f'g]="
{ e, f ²₁ gb =
{e, f²₁ fg} = 11
{e, 5², 3²g} =
11
11
"
"1
11
11
"
since f.f²g = fg-=9& { }
Since 1²g & {y
• Since f²fg.
f²f g - f³ g - g 4 2 3
Since f²f²g = f g = fg &{}
L>
71
Ee, g, fg} = not a subgp. since gffg)=ggf}=1²
#23
Ee, g, fg}=
Since g(8²) = g(gf) = f
483
E g, fg, fg}..
Since gf ggf) f
€23
So the only subgroups of order.
3 are <f>, < p ²>
11
2
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Transcribed Image Text:Are there any
other subgroups of
=
order 3 & 2 ? For his vere'll consider
all subsets of 3 and 2 elements
of $3 and use equations of fiz and
gf² = fg to check if they are subgroups
5-{e, f, f²g, fg, f²g]
}
All Subsets of 3 elements
{ e. f₁ f²} = < f> = < f ² >
{e₁
he₁ f₁ g y = Not a Subgp. Since £g¢{ }
2
17
{e, f, f'g]="
{ e, f ²₁ gb =
{e, f²₁ fg} = 11
{e, 5², 3²g} =
11
11
"
"1
11
11
"
since f.f²g = fg-=9& { }
Since 1²g & {y
• Since f²fg.
f²f g - f³ g - g 4 2 3
Since f²f²g = f g = fg &{}
L>
71
Ee, g, fg} = not a subgp. since gffg)=ggf}=1²
#23
Ee, g, fg}=
Since g(8²) = g(gf) = f
483
E g, fg, fg}..
Since gf ggf) f
€23
So the only subgroups of order.
3 are <f>, < p ²>
11
2
(1
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