Describe all nonisomorphic central extensions of Z_n by Z_2 x Z_2 meaning central group extensions of the following form
1 --> Z_n --> G --> Z_2 x Z_2 --> 1
Meaning, determine those nonisomorphic groups G that can be described by such an extension. Please also explain how you came up with the answer.
Solution Preview
The fact that Z_n is the kernel of the given inclusion amounts to the existence in G of an element a of order n (so that a generates Z_n). We know that G/<a> is Z_2xZ_2 so it is generated by two elements b,c of order 2 that commute. So G is any such group generated by a,b,c. Let's see what such groups we have:
Because Z_n is normal in G we know that b*a*(b^-1) belongs to Z_n (I denoted by * the group operation, and by b^-1 the inverse ...
... general domain to which our problem belongs ...Central Computer Verify the bank code and password ... case Perform invalid PIN extension Perform failed ...
... can be seen on either side of the central maximum when a ... To deal with this problem, he wears contact lenses that ... the lenses, this is simply an extension of the ...
... of mass M are connected by an extension less, uniform ... Use lagrangian/Hamiltonian Dynamics to solve this problem. ... only with each other by central forces can be ...
... state) and Ilesa West and Ife Central (Osun West ... and differential treatment, which by extension gets replicated ... Who are overwhelmed by the problems of extreme ...
... be engaged in without anyone finding out is a problem. ... go bad, the family served as a central location for ... com/articles/art29820.asp http://extension.usu.edu ...
... The US Central Intelligence Agency (CIA) estimates that as ... and use of contraceptive ARE WE THE PROBLEM? ... the debate altogether.40 By simple extension, the pro ...
... market by product development and line extensions entirely within ... the first time took a central role in ... enactment underlined that: The problem has rather an ...
... of the players that amplify the problem, to the ... One of the central, but most complicated, principles of ...Extension of Exchange Expiration Date for Private Debt ...
... Federal Express v. Holowecki, the central question before ... of Legal, Ethical and Regulatory Issues, Volume 12 ... the opportunity for a temporary extension of health ...
... for a mass audience, and has as a central aim the ... will always lack something still leaves problems, because the ... post-Renaissance art, it is an extension of it. ...
