14. Prove or disprove (a). (H.)( (G, *), and H is an abelian subgroup ⇒ HAG. (b). (H,*) ≤ (G,*), and G is an abelian group = N(H) G. (c). All subgroups of an abelian group are normals. (d). All subgroups of group with prime order are normals. (e). If (G, *) a group and HG such that G/H is finite G is finite. (f). There are 6 normal subgroups in the dihedral group D4. lack o
14. Prove or disprove (a). (H.)( (G, *), and H is an abelian subgroup ⇒ HAG. (b). (H,*) ≤ (G,*), and G is an abelian group = N(H) G. (c). All subgroups of an abelian group are normals. (d). All subgroups of group with prime order are normals. (e). If (G, *) a group and HG such that G/H is finite G is finite. (f). There are 6 normal subgroups in the dihedral group D4. lack o
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.8: Some Results On Finite Abelian Groups (optional)
Problem 14E: Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic...
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Transcribed Image Text:14. Prove or disprove
(a). (H,
(G, *), and H is an abelian subgroup ⇒ HAG.
(b), (H. *) ≤ (G, *), and G is an abelian group ⇒ N(H) - G.
(c). All subgroups of an abelian group are normals.
(d). All subgroups of group with prime order are normals.
(e). If (G, *) a group and HG such that G/H is finite G is
finite.
(f). There are 6 normal subgroups in the dihedral group D₁.
lack o
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