query: Algebra: Does every group whose order is a power of a prime p contain an element of order p?
positive_passages.docid: 19668
positive_passages.text: Does every group whose order is a power of a prime p contain an element of order p?
negative_passages.docid: 99205
negative_passages.text: Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
negative_passages.docid: 41731
negative_passages.text: Question about the order of the product of two elements in an abelian group
negative_passages.docid: 38853
negative_passages.text: Cyclic group of prime order
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: 15526
negative_passages.text: Question on groups of order $pq$
negative_passages.docid: 38153
negative_passages.text: Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
negative_passages.docid: 85579
negative_passages.text: $G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
negative_passages.docid: 66877
negative_passages.text: Showing groups of order $p^{k}(p+1)$ are not simple, p prime
negative_passages.docid: 4402
negative_passages.text: Group of order $pqr$, $p < q < r$ primes
negative_passages.docid: 91287
negative_passages.text: Is $G/pG$ is a $p$-group?
negative_passages.docid: 122125
negative_passages.text: Order of group element divides order of finite group
negative_passages.docid: 84789
negative_passages.text: Order of products of elements in a finite Abelian group
negative_passages.docid: 104080
negative_passages.text: Group with order $pq$ has subgroups of order $p$ and $q$
negative_passages.docid: 121423
negative_passages.text: Prove that every element of a finite group has an order
negative_passages.docid: 100605
negative_passages.text: let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in G$
negative_passages.docid: 121481
negative_passages.text: Non-abelian finite $p$-group in which every element has prime order?