An example of a semidirect product of a Q-group by a P-group by which is not a direct product

Abstract

Bu makalede $m\geq 3$ ve p,q tek asallar olmak üzere üssü $q^{m-1}$ olan q-Sylow altgrubu normal olan $p^nq^m$ mertebeli G grubu için $p\mid q-1$ ise G nin q-Sylow altgrubu Q ile p-Sylow altgrubu P nin direkt çarpımı olamayacağına dair bir örnek verildi.

In this paper, it is given an example of a group G of order $p^nq^m$ where $m\geq 3$ and p, q odd primes and the q-Sylow subgroup of G is normal in G and has exponent $q^{m-1}$ and $p\mid q-1$, then G cannot be the direct product of q-Sylow subgroup Q by p-Sylow subgroup P .