Any finite group has an even number of elements

Thread starter mathpr
Start date Nov 19, 2008
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Elements even Finite Group

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The statement that any finite group has an even number of elements is false; finite groups can have an odd number of elements. The existence of a field containing exactly 4 elements is true, as such a field can be constructed using the finite field GF(4). The dimension of a finite-dimensional vector space is not necessarily divisible by the dimension of any subspace, making that statement false as well. The discussion emphasizes the importance of understanding the properties of groups and vector spaces in abstract algebra. Overall, the statements prompt critical thinking about fundamental concepts in these mathematical areas.

Nov 19, 2008

mathpr

state whether the following statements are ture or false. give reason for that,
1. any finite group has an even number of elements.
2. there exists a field containing exactly 4 elements.
3. the dimension of a finite dimensional vector space is dividible by the dimension of any subspace.

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Nov 19, 2008

morphism

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Have you given these any thought? They're pretty trivial.

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