40 Is $n! + 1$ often a prime? 33 A group with five elements is Abelian 19 System of nonlinear equations that leads to cubic equation 14 Visually stunning math concepts which are easy to explain 14 Abelian Group Not Finitely Generated

### Reputation (35,000)

 +10 $N_G (P \cap Q)$ has more than one Sylow p-Subgroup under some conditions. +10 If a group contains a subgroup with the order of each of its divisors, is it abelian? +10 Normalizers of Sylow p-subgroups +10 Problem 2.16 - Character theory by Isaacs

### Questions (18)

 206 How can a piece of A4 paper be folded in exactly three equal parts? 16 Generalization of index 2 subgroups are normal 16 Subrings of finite index and units 14 Applications of the fact that a group is never the union of two of its proper subgroups 12 Finite groups of which the centralizer of each element is normal.

### Tags (163)

 2k group-theory × 960 115 abelian-groups × 48 1k abstract-algebra × 565 99 representation-theory × 61 728 finite-groups × 321 80 permutations × 19 264 sylow-theory × 153 75 characters × 39 122 normal-subgroups × 83 70 elementary-number-theory × 19

### Bookmarks (11)

 31 Find $\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\cdots}}}}$ 9 Example of a Subgroup That Is Not Normal 7 Index of subgroups in a finite solvable group, with trivial Frattini subgroup (Exercise 3B.12 from Finite Group Theory, by M. Isaacs) 4 If $H$ and $K$ are normal subgroups of $G$ and $H \cong K$, prove that $G/H \cong G/K$. 3 $G$ is a group with a normal subgroup $K$ such that $G/K$ is soluble, and $H$ is a nonabelian simple subgroup of $G$, then $H \leq K$