a.) What’s special about a normal subgroup? b.) When we say xH = Hx where H is a normal subgroup of G and x is an element of G, what exactly does that mean? c.) If y is an element of xH, what do we...

a.) What’s special about a normal subgroup?

b.) When we say xH = Hx where H is a normal subgroup of G and x is an element of G, what exactly does that mean?

c.) If y is an element of xH, what do we know about y? If y is also an element of Hx, what do we know about y?

d.) How are these two “facts” linked together by the “=”?