MHB Finite abelian group textbook help

caffeinemachine
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I need to read about finite abelian groups.

I searched 'finite abelian group' on amazon and the closest search result was 'finite group theory'. Googling didn't help either.

Does there exist a book dedicated to finite abelian groups? If yes, and if you know of a good one then please reply.

Right now I am primarily concerned with the action of $\text{Aut}(A)$ on $A$ where $A$ is a finite abelian group. If you know of a good source of literature in this particular topic then please help.
 
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I doubt there will be books written exclusively on finite abelian groups, because finite abelian groups are quite well characterized by the results here. Also, I have not read it, but this might be of interest.
 

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##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
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Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
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Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
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