# Tagged Questions

Abstract algebra is the study of algebraic objects. Some of the more common algebraic objects are groups, rings, fields, vector spaces, modules, among other topics.

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### Is there a redundant assumption in Exercise 2, page 14, from Janusz “Algebraic Number Fields”?

The exercise says: Let $R$ be an integral domain with quotient field $K$ and let $M$ be an $R$-submodule of a finite dimensional $K$-vector space. Prove $M=\bigcap_{P} R_P M$, where the ...
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### $\mathbb{Z}$ has no composition series. Need an assistance in some questions.

Please, read the whole post before trying to answer. Remark: here $\subset$ means "strict inclusion". I need to prove that the group $\mathbb{Z}$ has no composition series. That is, no normal series ...
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### There are 267 not isomorphic groups of order 64. How many of these are Abelian? Describe them. [closed]

There are 267 not isomorphic groups of order 64. How many of these are Abelian? Describe them.
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### Group order 168 having a normal subgroup of order 4, then G has a normal subgroup of order 28.

Prove that if G is a group of order 168 that has a normal subgroup of order 4, then G has a normal subgroup of order 28. resolution: P4 is the ordeme subgroup 4 and P7 the order subgroup 7. As P4 is ...