3) a € G a? = e for all We know that > then is Abeliem group. For any an arbitrary 2E z* , if bor all a E G, an = e does this imply is A bebon group ? an give counter example . Prove and be

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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a € G
a? = e
for alu
3)
We
that
know
any
Abelim
group . For
then
G
is
an
all a e G ,
α e
bor
arbitrary
2E Z*
it
A belion
group ?
imply
G
is
an
does
this
example -
give
Counter
Prove
and
ghoup
and H be
4)
Let
be
cyclic
Prove
that
H is
OL
subgroup of
G/H
is cyclić
Narmal
and
Subgroup
is
in
cyci
OY
this imply oa
does
Conver sly ib
is
yclie. Prove
Counter exarmple?
Transcribed Image Text:a € G a? = e for alu 3) We that know any Abelim group . For then G is an all a e G , α e bor arbitrary 2E Z* it A belion group ? imply G is an does this example - give Counter Prove and ghoup and H be 4) Let be cyclic Prove that H is OL subgroup of G/H is cyclić Narmal and Subgroup is in cyci OY this imply oa does Conver sly ib is yclie. Prove Counter exarmple?
QNO 1
:-
Let G
a E G. Is <a>
be
a.
group
and
Counter
example?
드 C어 (a) 2
Prove
grve
2) Let
be
subgroup
be
group
and
H, K
a
아
Relate
H and K
G
S.t
NG CH) = NG (K)
%3D
Transcribed Image Text:QNO 1 :- Let G a E G. Is <a> be a. group and Counter example? 드 C어 (a) 2 Prove grve 2) Let be subgroup be group and H, K a 아 Relate H and K G S.t NG CH) = NG (K) %3D
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