Lec-4 ,Theorem :- A field is finite iff it's multiplicative group is cyclic. #FieldExtension
Theorem :- A field is finite iff it's multiplicative group is cyclic.
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lec-5 If F is a field with p^n elements.Then F has a subfield F' with p^m elements iff m divides n.
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![Theorem- Finite extension of a finite extension is also finite extension || [L:F] = [L:K] [K:F]](https://i.ytimg.com/vi/1lIBPS894ns/hqdefault.jpg?sqp=-oaymwE9CNACELwBSFryq4qpAy8IARUAAAAAGAElAADIQj0AgKJDeAHwAQH4Af4JgALQBYoCDAgAEAEYZSBOKEgwDw==&rs=AOn4CLB1Zly2ezMJTFzJCAypcy7ECWUmzg)
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Theorem- Finite extension of a finite extension is also finite extension || [L:F] = [L:K] [K:F]
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multiplicative group of non- zero elements of finite field forms a cyclic group. proof in telugu
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