|Aut (L/K) = |Aut(L)|–|Aut(K)|. x)
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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Answer part (x) only
![1.
Which of the following statements are true? Give reasons for your answers.
In a non-abelian group of order 27, the identity conjugacy class is the only class with
a single element.
i)
A finite field with 16 elements has a subfield with 8 elements.
iji)
The number of distinct abelian groups of order p"p"?
-P* is n,n,...ng, where the
...
P; are distinct primes and n, e N.
in) If G is a finite group, such that Z(G) = G, then o(G) is a prime.
If X is a G-set, Ga group, and YCX is G-invariant, then X\Y is G-invariant.
i) Any group of order 202 is simple.
yii) SL,(R) C0(3).
Viii) If R is an integral domain, then R/I is an integral domain, for any ideal I of R.
Every prime element of Z[x,,x,,.,x,] is irreducible.
x) |Aut (L/K) = |Aut(L)-|Aut(K).
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb1f115b-cbb4-4f96-a28c-b814570ea454%2Fcc6c0abc-2625-494d-aec0-716f1e5396e0%2Fmg1mtkc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
Which of the following statements are true? Give reasons for your answers.
In a non-abelian group of order 27, the identity conjugacy class is the only class with
a single element.
i)
A finite field with 16 elements has a subfield with 8 elements.
iji)
The number of distinct abelian groups of order p"p"?
-P* is n,n,...ng, where the
...
P; are distinct primes and n, e N.
in) If G is a finite group, such that Z(G) = G, then o(G) is a prime.
If X is a G-set, Ga group, and YCX is G-invariant, then X\Y is G-invariant.
i) Any group of order 202 is simple.
yii) SL,(R) C0(3).
Viii) If R is an integral domain, then R/I is an integral domain, for any ideal I of R.
Every prime element of Z[x,,x,,.,x,] is irreducible.
x) |Aut (L/K) = |Aut(L)-|Aut(K).
%3D
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