Is there a theorem that can help us count easily the number of subgroups of any given finite group?
Is there a theorem that can help us count easily the number of subgroups of any given finite group?
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abstract-algebra
group-theory
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1@Rasmus: You would then have $a=b^i$ and $a^j=b$, so $a$ and $b$ both have order
finite. In an infinite group you either have an element of infinite order, or infinitely many elements of finite order. This means that every infinite group has infinitely many subgroups. – 2012-10-25
1 Answers
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Here is a partial answer by G.A. Miller: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1077761/pdf/pnas01604-0036.pdf
It turns out that there is a way to count the subgroups of any given Abelian group.