6

In the theory of finite abstract group, abelianness-forcing number $n$ is characterized as a positive integer with standard factorization $n=p_1^{k_1}p_2^{k_2}\cdots p_r^{k_r}$ with $k_i \le 2$ and $p_i$ does not divide $p_j^{k_j}-1$ for any $1 \le i,j \le r$. I want to define a function "AbeliannessForcingNumberQ" which returns "True" if and only if the argument is a abeliannes-forcing number. But I cannot figure out how to deal with prime factors and exponents in a given number. Please help to define this function.

The following is an external link for the corresponding mathematical concept. https://groupprops.subwiki.org/wiki/Abelianness-forcing_number

– seoneo – 2019-07-09T22:46:39.390