query: If $G$ is a group of order $p^2$ with $p$ a prime number then $G \simeq C_{p^2}$ or $G \simeq C_p \times C_p$
positive_passages.docid: 152481
positive_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: 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: 39976
negative_passages.text: If a group G has only the trivial group and G itself as its subgroup, can we be sure that G has prime order?
negative_passages.docid: 106577
negative_passages.text: If G is not abelian with order $p^3$ then $G'=Z(G)$
negative_passages.docid: 56607
negative_passages.text: gcd and order of elements of group
negative_passages.docid: 117468
negative_passages.text: $o(g^{k})=\frac{o(g)}{\gcd(o(g),k)}$ order of a power of a group element.
negative_passages.docid: 141890
negative_passages.text: $G$ is a Group of order $pq$, if $G$ has exactly one subgroup of order $p$ and another with order $q$, then $G$ is cyclic ($p,q$ are prime)
negative_passages.docid: 83710
negative_passages.text: Order of a homomorphism of groups
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: 110390
negative_passages.text: Order of group $GL_{2}\left( \mathbb{F}_{p}\right) $
negative_passages.docid: 13734
negative_passages.text: Show that every group of prime order is cyclic
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: 53207
negative_passages.text: Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
negative_passages.docid: 57427
negative_passages.text: Group of order $8p$ is solvable, for any prime $p$
negative_passages.docid: 137186
negative_passages.text: Let G be $\mathbb Z_p\times\dots\times \mathbb Z_p$ . Find A(G).
negative_passages.docid: 79995
negative_passages.text: G is group of order pq, pq are primes
negative_passages.docid: 121481
negative_passages.text: Non-abelian finite $p$-group in which every element has prime order?