# Questions tagged [subgroup-growth]

Subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group.

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### Why isn't the growth of $\mathrm {Iso}(\mathbb R ^2)$ sub-exponential? [closed]

Given a finite subset $S$ of a group, denote by $\gamma_S(n)$ the number of distinct elements that are words of length $n$ in $S\cup S^{-1}$. A group is of sub-exponential growth if for every finite ...
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### From an anual growth rate to a monthly compunded

Let's say I have an amount that grew in 1 year of 5%. From 100, to 105. How do I calulcate the average monthly growth? Using the CAGR, I could write: $(105/100)^{1/12}-1 = 0.41\%$ Is this formula ...
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### All subgroups of a group with order the square of a prime

So I have a group of order $p^2$ (where $p$ is a prime number) and I'm wondering how many subgroups it can have. By Lagrange's theorem I know that if a subgroup exists its order has to divide the ...
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### Wreath product of subgroup with symmetric group

I am going through Generic Quantum Fourier Transforms by Moore et al. I would like to put the screenshot of the section I am confused about below. So, Why does $H$ need to be of size $poly(n)$ for ...
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### Getting 25% growth over last year sale

I want to calculate 25% growth over prior year's sale (by month). The way I am solving this currently is by multiplying (sale)*1.25; this works fine for sale values that are positive but for those ...