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Let G be a group with |G| = 96. Suppose H and K are subgroups of G with H| = 12 and K| = 16. Then (a) HOK = {e} (d) HnK is not Abelian (b) HOK + {e} (c) HOK is Abelian

Let G be a group with |G| = 96. Suppose H and K are subgroups of G with H| = 12 and K| = 16. Then (a) HOK = {e} (d) HnK is not Abelian (b) HOK + {e} (c) HOK is Abelian

Advanced Engineering Mathematics
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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Thus option (c) is correct. Let G be a group with G| = 96. Suppose H and K are subgroups of G with H] = 12 and K| = 16. Then (a) HOK = {e} (b) HnK # {e} (c) HOK is Abelian (d) HnK is not Abelian
Transcribed Image Text:Thus option (c) is correct. Let G be a group with G| = 96. Suppose H and K are subgroups of G with H] = 12 and K| = 16. Then (a) HOK = {e} (b) HnK # {e} (c) HOK is Abelian (d) HnK is not Abelian
s'i b): Consider the set of matrices G= Z,s €{-1,+1} Then which of the following is true? (a) G forms a group under addition (b) G forms an abelian group under multiplication (c) Every element in G is diagonalizable over C. (d) G is a finitely generated group under multiplication.
Transcribed Image Text:s'i b): Consider the set of matrices G= Z,s €{-1,+1} Then which of the following is true? (a) G forms a group under addition (b) G forms an abelian group under multiplication (c) Every element in G is diagonalizable over C. (d) G is a finitely generated group under multiplication.
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