Suppose that a group G has a subgroup of order n. Prove that the intersection of all subgroups of G of order n is a normal subgroup of G.

BiolK103 Notes Chapter 21: The Origin and Evolutionary History of Life 1) Formation of Organic Molecules a) Reactive Surfaces i) Pyrite (fool’s gold) ii) Clay (1) Charged surfaces + + (2) Ions (Zn and Fe ) [Catalysts] (3) Enzymelike features iii) Surface attract monomers that spontaneously polymerize b) Prebiotic Soup Hypothesis i) Organic molecules formed near Earth’s surface in “sea of organic soup” (1) Spontaneously reacting to each other c) IronSulfur World Hypothesis i) Organic precursors formed near hydrothermal vents (1) Energyrich molecules and precursors of biological molecules (2) Communities [tube worms and other