query: Hungerford Chapter 2 Section 2 Problem 2 WITHOUT using the structure theorem of finite abelian groups
positive_passages.docid: 25235
positive_passages.text: Finite abelian groups - direct sum of cyclic subgroup
negative_passages.docid: 125640
negative_passages.text: Group of order $p^2$ is abelian.
negative_passages.docid: 114662
negative_passages.text: Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
negative_passages.docid: 5741
negative_passages.text: Direct product of abelian groups
negative_passages.docid: 151619
negative_passages.text: A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic
negative_passages.docid: 62277
negative_passages.text: Cayley tables for two non-isomorphic groups of order 4.
negative_passages.docid: 98474
negative_passages.text: Show the existence of a certain subgroup of F2
negative_passages.docid: 128692
negative_passages.text: Example of an infinite group where every element except identity has order 2
negative_passages.docid: 134455
negative_passages.text: Any group of order $15$ is abelian(without sylow theorem)
negative_passages.docid: 115973
negative_passages.text: Computing the number of nonisomorphic finite abelian groups of order $n$
negative_passages.docid: 65900
negative_passages.text: Show that a finite group with certain automorphism is abelian
negative_passages.docid: 15341
negative_passages.text: Non-abelian finite group in which more than half of the elements have order $2$
negative_passages.docid: 108425
negative_passages.text: Problem on abelian group
negative_passages.docid: 137931
negative_passages.text: Problem from "The Theory of Finite Groups" by Kurzweil and Stellmacher
negative_passages.docid: 104112
negative_passages.text: Number of finite simple groups of given order is at most $2$ - is a classification-free proof possible?
negative_passages.docid: 157585
negative_passages.text: Structure theorem of finite rings
negative_passages.docid: 47623
negative_passages.text: The set of all complex homomorphisms of abelian group $G$ has the same structure as $G$