query: Show that $S_n$ has elements of order $p^t \Longleftrightarrow n \geq p ^t$, being $n, t$ positive integers and $p$ a prime number.
positive_passages.docid: 157806
positive_passages.text: Order of a element on a Symmetric Group
negative_passages.docid: 34491
negative_passages.text: Is there a way to show that $\sqrt{p_{n}} < n$?
negative_passages.docid: 61550
negative_passages.text: Existence of elements of order $p^k$ in a finite group
negative_passages.docid: 126893
negative_passages.text: A group of order 2p (p prime) and other conditions - prove abelian.
negative_passages.docid: 25835
negative_passages.text: Structure of groups of order $pq$, where $p,q$ are distinct primes.
negative_passages.docid: 88656
negative_passages.text: For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
negative_passages.docid: 68201
negative_passages.text: Cyclic group of order $n$
negative_passages.docid: 13734
negative_passages.text: Show that every group of prime order is cyclic
negative_passages.docid: 15000
negative_passages.text: Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
negative_passages.docid: 16660
negative_passages.text: Prove that any positive number has an $n$th root
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: 27784
negative_passages.text: Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.
negative_passages.docid: 44019
negative_passages.text: Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
negative_passages.docid: 2614
negative_passages.text: Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$
negative_passages.docid: 41709
negative_passages.text: Show that the symmetric group $S_p = $, where $\sigma$ is any transposition and $\tau$ is any p- cycle and p is a prime number.
negative_passages.docid: 119486
negative_passages.text: Upper and Lower bounds on the nth prime number
negative_passages.docid: 21568
negative_passages.text: Maximal order of an element in a symmetric group