Group Orders That Imply Existence Of Nontrivial Normal p-Subgroups

Mathematics – Group Theory

Scientific paper

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6 pages

Scientific paper

Given a prime $p$ and a natural number $n$, we provide simple divisibility
criterions that determine whether all solvable group of order $n$ have a
nontrivial normal $p$-subgroup, or there is exactly one group of order $n$
without nontrivial normal $p$-subgroups.

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