query: The order of a non-abelian group is $pq$ such that $p<q$. Show that $p\mid q-1$ (without Sylow's theorem)
positive_passages.docid: 8746
positive_passages.text: Groups of order $pq$ without using Sylow theorems
negative_passages.docid: 15210
negative_passages.text: Group of order 6 proof
negative_passages.docid: 79995
negative_passages.text: G is group of order pq, pq are primes
negative_passages.docid: 133272
negative_passages.text: Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
negative_passages.docid: 18182
negative_passages.text: An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
negative_passages.docid: 108309
negative_passages.text: An example of a non-abelian group of order $p^3$
negative_passages.docid: 116080
negative_passages.text: Let G be a finite group with more than one element. Show that G has an element of prime order
negative_passages.docid: 85106
negative_passages.text: Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
negative_passages.docid: 85011
negative_passages.text: Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
negative_passages.docid: 92899
negative_passages.text: $G$ is non abelian simple group of order $<100$ then $G\cong A_5$
negative_passages.docid: 123796
negative_passages.text: Order of automorphism group of a $p$-group is divisible by $p$.
negative_passages.docid: 21673
negative_passages.text: If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
negative_passages.docid: 101735
negative_passages.text: A finite $p$-group cannot be simple unless it has order $p$
negative_passages.docid: 13807
negative_passages.text: Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S
negative_passages.docid: 13742
negative_passages.text: Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
negative_passages.docid: 62977
negative_passages.text: Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
negative_passages.docid: 81543
negative_passages.text: Finite abelian group contains an element with order equal to the lcm of the orders of its elements