Let a be an element of a group G such that Ord(a) = 32. If H is a normal subgroup of G, then Ord(aH) could be * O 8 O 6 O 4 O None of the choices

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Q: Let a be an element of a group G such that Ord(a) = 30. If H is a normal subgroup of G, then Ord(aH)…

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A: Consider the provided question, According to you we have to solve only question no. 2. (2)

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A: We know that b∈bH                                    (1) We know that aH = bH if and only if a-1b∈H…

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Q: Let H be a subgroup of a group G and a, b E G. Then be aH if and only if *

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Q: Let a be an element of a group G such that Ord(a) = 32. If H is a normal subgroup of G, then Ord(aH)…

A: As you asked multiple questions , I answered only first question.   Here we can say from a corollary…

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Q: If G is a finite group with |G|<120 and G has subgroups of orders 1O, 15 and 20 then the order of G…

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Q: If G is a finite group with |G|<180 and G has subgroups of orders 10, 18 and 30 then the order of G…

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Q: Let H be a subgroup of a group G and a, be G. Then b E aH if and only if ab-1 e H O ab e H O None of…

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Q: If G is a finite group with |G|<120 and G has subgroups of orders 10, 15 and 20 then the order of G…

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Q: Let a be an element of a group G such that Ord(a) = 30. If H is a normal subgroup of G, then Ord(aH)…

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Q: 1. Let G be a group and let H, H, .. H, be the subgroups of G. The ...

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Q: Suppose that G is a group such that Ord(G) = 36. The number of subgroups %3D that G has is 4 О 12 О…

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