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 9 $G$ group and $H,K \le G$, with $H,K \ne \lbrace e \rbrace$. Does $H \cap K \cong K$ imply $H \cap K = K$? 8 Minimum value of $\sqrt{x^2+25}+\sqrt{y^2+16}$ if $x+y=12$ 6 Are all nilpotent groups hamiltonian? 6 Suppose $AN_1=AN_2=G$, $A\cap N_1=A\cap N_2=1$ and $N_1,N_2$ are normal in $G$, do we have $N_1\cong N_2$? 6 Proof (or counter-example) of the existence of an element of order $p$ in a conjugacy class $aH$ of a subgroup $H$ of a finite group $G$

### Reputation (1)

 +25 An exercise in an introduction to the theory of groups +10 $G$ group and $H,K \le G$, with $H,K \ne \lbrace e \rbrace$. Does $H \cap K \cong K$ imply $H \cap K = K$? +2 weak-topology tag wiki +2 weak-topology tag wiki excerpt

### Questions (3)

 6 Hall subgroups of $\mathrm{PSL}$ 5 The number of groups $G$ (up to isomorphism) such that $G/\mathbb{Z}_3\cong D_{2n}$ 5 Can $A_n$ be generated by two elements $x,y$ with $x\ne 1$ arbitrarily chosen?

### Tags (43)

 102 group-theory × 35 11 normal-subgroups × 6 68 abstract-algebra × 26 10 abelian-groups × 3 32 finite-groups × 12 7 matrices × 4 21 algebra-precalculus × 5 7 sylow-theory × 3 14 linear-algebra × 7 7 cyclic-groups × 2