Let G be a finite group, i.e., |G| < ∞. 1). of the subgroup (a²) of G in G Let |G| = 360. Let a E G and |a| = 60. Find the number of left cosets 2). of G, i.e., K
Let G be a finite group, i.e., |G| < ∞. 1). of the subgroup (a²) of G in G Let |G| = 360. Let a E G and |a| = 60. Find the number of left cosets 2). of G, i.e., K
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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Transcribed Image Text:Let G be a finite group, i.e., |G| < o∞.
(1). Let |G| = 360. Let a e G and |a| = 60. Find the number of left cosets
of the subgroup (a²) of G in G
(2). Let K be a proper subgroup of H and let H be a proper subgroup
of G, i.e., K <H and H < G. It is known
(a). |K| = 30,
(b). |G| = 300, and
(c). there exists an element a E H with |a| = 25
%3D
Determine the possible order(s)of H, i.e., |H|.
Expert Solution

Step 1 Given
A finite group i.e.,
To Find- the no. of cosets of the subgroup of G in G
- the possible order(s) of H , i.e.,. for K , a proper subgroup of H be a proper subgroup of G i,e, K < H and H< G. it is known (a)
(b)
(c) there exists an element
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