query: Every group of order $56$ has a proper non - trivial normal subgroup?
positive_passages.docid: 141188
positive_passages.text: Groups of order $56$
negative_passages.docid: 101602
negative_passages.text: consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
negative_passages.docid: 61373
negative_passages.text: A normal subgroup that is not a characteristic
negative_passages.docid: 8066
negative_passages.text: Sort-of-simple non-Hopfian groups
negative_passages.docid: 157841
negative_passages.text: Existence of a non-abelian group of order $p^n$.
negative_passages.docid: 50762
negative_passages.text: If $S_n$ has cyclic subgroups of these orders or not?
negative_passages.docid: 115204
negative_passages.text: Show that SO(n) is a normal subgroup of O(n)
negative_passages.docid: 29996
negative_passages.text: Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
negative_passages.docid: 148904
negative_passages.text: Groups of order $p^3$
negative_passages.docid: 23533
negative_passages.text: All subgroups normal $\implies$ abelian group
negative_passages.docid: 44165
negative_passages.text: the image of normal subgroups
negative_passages.docid: 75590
negative_passages.text: How many normal subgroups does a non-abelian group $G$ of order $ 21$
negative_passages.docid: 151727
negative_passages.text: If $|G/H|=4$ then $G$ is union of three proper subgroups
negative_passages.docid: 8746
negative_passages.text: Groups of order $pq$ without using Sylow theorems
negative_passages.docid: 68201
negative_passages.text: Cyclic group of order $n$
negative_passages.docid: 46940
negative_passages.text: On Groups of Order 315 with a unique sylow 3-subgroup .
negative_passages.docid: 121481
negative_passages.text: Non-abelian finite $p$-group in which every element has prime order?