query: How to calculate the order of multiplicative group $\mathbb{Z}^{*}_{p^x}$ where $p$ is a prime and $x$ is any positive integer ???
positive_passages.docid: 15000
positive_passages.text: Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
negative_passages.docid: 31380
negative_passages.text: Exponent and abelian groups
negative_passages.docid: 70001
negative_passages.text: Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)
negative_passages.docid: 37929
negative_passages.text: Classification of prime ideals of $\mathbb{Z}[X]$
negative_passages.docid: 108830
negative_passages.text: Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
negative_passages.docid: 122312
negative_passages.text: How can I compute $\mathrm{Aut}(\mathbb{Z}/4\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z})$?
negative_passages.docid: 122125
negative_passages.text: Order of group element divides order of finite group
negative_passages.docid: 131971
negative_passages.text: If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.
negative_passages.docid: 50412
negative_passages.text: Prime elements in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 51373
negative_passages.text: $G$ non abelian, order $p^3$ ($p$ prime). Suppose that the center is $p^2$, prove that $\exists\ x$ outside of the center, of order p
negative_passages.docid: 152481
negative_passages.text: If order of group is $p^2$, where $p$ is prime, how can you deduce $G$ is isomorphic to $C_{p^2}$ or $C_p \times C_p$?
negative_passages.docid: 126893
negative_passages.text: A group of order 2p (p prime) and other conditions - prove abelian.
negative_passages.docid: 43580
negative_passages.text: Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
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: 55429
negative_passages.text: Why does a Galois field have to have an order of $p^n$ where $p$ is prime?
negative_passages.docid: 125640
negative_passages.text: Group of order $p^2$ is abelian.
negative_passages.docid: 15526
negative_passages.text: Question on groups of order $pq$