query: $\lvert G\rvert=24$ not simple by a counting arguments
positive_passages.docid: 26449
positive_passages.text: $|G|=24$ prove that $G$ is not simple
negative_passages.docid: 135808
negative_passages.text: Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
negative_passages.docid: 97878
negative_passages.text: Are there uncountably many surjections from $\mathbb N$ to $\mathbb N$?
negative_passages.docid: 117899
negative_passages.text: At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic
negative_passages.docid: 68308
negative_passages.text: A (probably trivial) induction problem: $\sum_2^nk^{-2}\lt1$
negative_passages.docid: 151029
negative_passages.text: The number of non normal subgroups of a group cannot be $1$?
negative_passages.docid: 156319
negative_passages.text: Show that a group with $|G| = 33$ contains an element of order $3$
negative_passages.docid: 89415
negative_passages.text: Number of homomorphisms from $(\mathbb Q^+ , \,\cdot\,)$ to $(\mathbb Z_n , +)$
negative_passages.docid: 104349
negative_passages.text: Proof by induction involving symmetric groups
negative_passages.docid: 119152
negative_passages.text: Proving irreducibility of $x^6-72$
negative_passages.docid: 131031
negative_passages.text: Q: Proving G is d-colorable
negative_passages.docid: 62455
negative_passages.text: Prove Equivalence Relation in G
negative_passages.docid: 18160
negative_passages.text: How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
negative_passages.docid: 116737
negative_passages.text: An element of a group $G$ is not conjugate to its inverse if $\lvert G\rvert$ is odd
negative_passages.docid: 43113
negative_passages.text: Whether the given number is divisible by 24?
negative_passages.docid: 16172
negative_passages.text: My proof of $I \otimes N \cong IN$ is clearly wrong, but where have I gone wrong?
negative_passages.docid: 129157
negative_passages.text: An exercise on isomorphic groups of order 24