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Group Orders That Imply Existence Of Nontrivial Normal p-Subgroups

Research paper by Rafael Villarroel-Flores

Indexed on: 22 Nov '04Published on: 22 Nov '04Published in: Mathematics - Group Theory



Abstract

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.