1. Let (G, *) be a finite group of order n. Then (a). Let n = pq (p, q are a prime numbers) and let H, K ≤ G (unique subgroups) such that |H| = p, |K| = q. Then G is cyclic group. (b). If n = ph (p is a prime number, and he Z+), then G has an
1. Let (G, *) be a finite group of order n. Then (a). Let n = pq (p, q are a prime numbers) and let H, K ≤ G (unique subgroups) such that |H| = p, |K| = q. Then G is cyclic group. (b). If n = ph (p is a prime number, and he Z+), then G has an
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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![1. Let (G, *) be a finite group of order n. Then
(a). Let n = pq (p, q are a prime numbers) and let H, K≤ G (unique
subgroups) such that |H| = p, |K| = q. Then G is cyclic group.
(b). If n = ph (p is a prime number, and he Z+), then G has an
BL
akh
U...
Lo...
matics
Mux
element of order p.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5bdf6563-82b9-4ba8-8abc-41bfa41ce6bc%2F68f30b1f-2111-48c1-9501-60fdecd56507%2Faki9d6o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let (G, *) be a finite group of order n. Then
(a). Let n = pq (p, q are a prime numbers) and let H, K≤ G (unique
subgroups) such that |H| = p, |K| = q. Then G is cyclic group.
(b). If n = ph (p is a prime number, and he Z+), then G has an
BL
akh
U...
Lo...
matics
Mux
element of order p.
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