query: Existence of a normal p-Sylow subgroup when $\lvert\mkern1mu G\mkern1mu \rvert=q^{2}\mkern1mu p$
positive_passages.docid: 90449
positive_passages.text: Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.
negative_passages.docid: 78553
negative_passages.text: A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$
negative_passages.docid: 23533
negative_passages.text: All subgroups normal $\implies$ abelian group
negative_passages.docid: 61373
negative_passages.text: A normal subgroup that is not a characteristic
negative_passages.docid: 42096
negative_passages.text: Direct product of Sylow subgroups
negative_passages.docid: 111375
negative_passages.text: Normality of subgroups and Sylow groups under homomorphisms...
negative_passages.docid: 46940
negative_passages.text: On Groups of Order 315 with a unique sylow 3-subgroup .
negative_passages.docid: 61550
negative_passages.text: Existence of elements of order $p^k$ in a finite group
negative_passages.docid: 15526
negative_passages.text: Question on groups of order $pq$
negative_passages.docid: 105139
negative_passages.text: Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
negative_passages.docid: 142413
negative_passages.text: Normal Subgroups of $SU(n)$
negative_passages.docid: 122335
negative_passages.text: Abelian $p$-group with unique subgroup of index $p$
negative_passages.docid: 36040
negative_passages.text: A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
negative_passages.docid: 115204
negative_passages.text: Show that SO(n) is a normal subgroup of O(n)
negative_passages.docid: 6134
negative_passages.text: Some Subgroup of Dihedral Group is Normal
negative_passages.docid: 2174
negative_passages.text: Proving that HK is a subgroup when K is normal
negative_passages.docid: 123677
negative_passages.text: Normal subgroups of infinite symmetric group