query: Equivalent condition for finite cyclic commutative group
positive_passages.docid: 2104
positive_passages.text: Finite group for which $|\{x:x^m=e\}|\leq m$ for all $m$ is cyclic.
negative_passages.docid: 25235
negative_passages.text: Finite abelian groups - direct sum of cyclic subgroup
negative_passages.docid: 25997
negative_passages.text: Conditions Equivalent to Injectivity
negative_passages.docid: 114187
negative_passages.text: In a finite cyclic group, the generator has the order of the group
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: 57887
negative_passages.text: When are the product of cyclic groups also cyclic?
negative_passages.docid: 88199
negative_passages.text: The commutator subgroup of a quotient in terms of the commutator subgroup and the kernel
negative_passages.docid: 48009
negative_passages.text: Left inverse implies right inverse in a finite ring
negative_passages.docid: 14255
negative_passages.text: Commutator subgroup and cyclic normal subgroup
negative_passages.docid: 157863
negative_passages.text: A finite pseudo-ring such that $ab^2=b$ for some $(a,b)\in A$
negative_passages.docid: 108330
negative_passages.text: Product of all elements in finite abelian group equals its own inverse
negative_passages.docid: 34183
negative_passages.text: An equivalent condition with $\{0\}$ being the only nilpotent ideal
negative_passages.docid: 150207
negative_passages.text: Non isomorphic subgroups of cyclic groups
negative_passages.docid: 84789
negative_passages.text: Order of products of elements in a finite Abelian group
negative_passages.docid: 61394
negative_passages.text: The product of finitely many cyclic groups is cyclic
negative_passages.docid: 73402
negative_passages.text: Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group
negative_passages.docid: 95867
negative_passages.text: Subgroup of $C^*$ (nonzero complex) with finite index.