Name: Julian Sanders 1) For these short answer questions, give a short concise one or two sentence reason/argument/calculation. Avoid long detailed proofs. (p) We have a circular bracelet made of 4 equally spaced beads. What is the number of different ways to paint the beads using 5 colors? (Two colorings of the bracelet are considered the same if we can get from one bracelet to the other by some combination of rotations and flips, and in any one coloring of the bracelet you can use 1, 2, 3, or 4 of the available colors.) Concise Reason (q) Let G be a finite group of order 315 = 32 x 5 x 7, and assume that H and K are subgroups of order 15 and 21 respectively. Then can (H, K) possibly not be a normal subgroup of G? Concise Reason P207
Name: Julian Sanders 1) For these short answer questions, give a short concise one or two sentence reason/argument/calculation. Avoid long detailed proofs. (p) We have a circular bracelet made of 4 equally spaced beads. What is the number of different ways to paint the beads using 5 colors? (Two colorings of the bracelet are considered the same if we can get from one bracelet to the other by some combination of rotations and flips, and in any one coloring of the bracelet you can use 1, 2, 3, or 4 of the available colors.) Concise Reason (q) Let G be a finite group of order 315 = 32 x 5 x 7, and assume that H and K are subgroups of order 15 and 21 respectively. Then can (H, K) possibly not be a normal subgroup of G? Concise Reason P207
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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Question
Transcribed Image Text:Name:
Julian Sanders
1) For these short answer questions, give a short concise one or two sentence reason/argument/calculation. Avoid long
detailed proofs.
(p) We have a circular bracelet made of 4 equally spaced beads.
What is the number of different ways to
paint the beads using 5 colors? (Two colorings of the bracelet are considered the same if we can get from one
bracelet to the other by some combination of rotations and flips, and in any one coloring of the bracelet you can
use 1, 2, 3, or 4 of the available colors.)
Concise Reason
(q) Let G be a finite group of order 315 = 32 x 5 x 7, and assume that H and K are subgroups of order 15 and 21
respectively. Then can (H, K) possibly not be a normal subgroup of G?
Concise Reason
P207
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