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Many books do not provide how to get all groups of order 16 (even not an exercise). Is there any good way to get the groups of order 16? I found 12 groups. But not getting remaining two. I found one article "Groups of order Sixteen Made easy", but his arguments are using something called cyclic extensions(Alas!! Is it necessary to use EXTENSIONS ?).

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7 
 Alas! it may be necessary to use complicated mathematics to answer easily posed questions. – Yemon Choi Jan 23 2011 at 4:56
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 What is the problem with using extensions? – Mariano Suárez-Alvarez Jan 23 2011 at 4:58
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 It is well worth conquering any fear you may have of extensions! – David Hansen Jan 23 2011 at 5:11
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 @Marshall Please don't shout. It is particularly unnecessary when addressing God, since he will probably hear you anyway (alas, I am not sure how helpful he will be with the particular problem at hand). – Alex Bartel Jan 23 2011 at 5:16
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 By the way, if you don't like extensions, then you can enumerate all potential multiplication tables and check which ones really define groups. It's a finite task after all. Deciding whether two such tables give isomorphic groups is also a finite task, since there is a finite number of bijections between any two such sets. Chances are that after that, you will love extensions. – Alex Bartel Jan 23 2011 at 5:18
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closed as too localized by Alex Bartel, Mariano Suárez-Alvarez, David Hansen, Pete L. Clark, Yemon Choi Jan 23 2011 at 5:36

1 Answer

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There is a book "Groups for Undergraduates" by John Moody, who has given classification of groups of order 16, without Extension Theory...he has used "Abelianization" process....it may be helpful....

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