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Questions on group theory which concern finite groups.
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votes
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answer
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views
Generalizing the Notion of Nilpotent/Abelian/Cyclic Numbers
Let us call a number $n\in\mathbb{N}$ nilpotent if
$$n=p_1^{e_1}\cdots p_m^{e_m}$$
with $p_i^k\not\equiv 1\mod p_j$ for $i,j\in\{1,\ldots,m\}$ and $1\leqslant k\leqslant e_i$.
A cute theorem says the …