I was reading this article called "On A Theorem of Frobenius: Solutions to $x^n=1$ in Finite Groups" by I.M. Isaacs and G.R. Robinson (www.jstor.org/stable/2324902).

In the third para of the first page they said that - " If $n>0$ is an integer, we shall write $n_p$ to denote the largest power of the prime $p$ which divides $n$. For example, $24_2=8$"

My question is that how can 8 be the largest power of 2 that divides 24, since $2^8=256$ ? I think I am getting confused somewhere... Can the above statement be thought of in any other way?

  • 1
    $\begingroup$ The statement means that $n_p$ is the biggest $p^{r}$ which divides $n$, not the exponent $r$. So $8 = 2^{3}$ divides $24$ but $16 = 2^{4}$ does not, hence $24_{2} = 8$. $\endgroup$ – Alastair Litterick Oct 22 '14 at 2:18
  • $\begingroup$ I see... now the statement seems to make sense to me.... Thanks Alastair... $\endgroup$ – Ritu Oct 22 '14 at 2:22

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