Group Theory (XXXVII): If N is a normal subgroup of G and H is any subgroup of G, prove that NH is a subgroup of G.

Modern Algebra Group Theory (XXXVII) Subgroups of a Group Normal Subgroups of a Group If N is a normal subgroup of G and H is any subgroup of G, prove that NH is a subgroup of G.

Group Theory (XXXVIII): To show that the intersection of two normal subgroups of G is a normal subgroup of G.

Modern Algebra Group Theory (XXXVIII) Subgroups of a Group Normal Subgroups of a Group To show that the intersection of two normal subgroups of G is a normal subgroup of G.

Group Theory (XXXIX): If H is a subgroup of G and N is a normal subgroup of G, show that H∩N is a normal subgroup of H.

Modern Algebra Group Theory (XXXIX) Subgroups of a Group Normal Subgroups of a Group If H is a subgroup of G and N is a normal subgroup of G, show that H∩N is a normal subgroup of H.

Group Theory (XL): Every subgroup of an abelian group is normal.

Modern Algebra Group Theory (XL) Subgroups of an Abelian Group Normal Subgroups of a Group Every subgroup of an abelian group is normal.

Group Theory (XLI): Suppose that N and M are two normal subgroups of G and that N∩M = (e).Show that for any nєN, mєM, nm = mn.

Modern Algebra Group Theory (XLI) Subgroups of a Group Normal Subgroups of a Group Suppose that N and M are two normal subgroups of G and that N∩M = (e) Show that for any nєN, mєM, nm = mn.