Question Number 129558 by mnjuly1970 last updated on 16/Jan/21
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{modern}\:\ast\ast\ast\ast\ast\ast\ast\ast\ast\ast\:{algebra}\:...\: \\ $$ $$\:\:\:\:\:\:\:\::::\:\:{if}\:\:''\:{G}\:''\:{be}\:{a}\:{finite}\:{group}\:{and} \\ $$ $$\:\:{O}\:\left({G}\right)={pq}\:\:,\:\:{where}\:''\:{p}\:,\:{q}\:''\:{are}\:{two} \\ $$ $$\:\:{prime}\:\:{numbers}\:\left({p}\:>\:{q}\:\right)\:{then}\:{prove}\:{that}: \\ $$ $$\:\:{G}\:\:{has}\:\:{at}\:{most}\:{one}\:{subgroup}\:{of}\:{order}\:''\:{p}\:''\:. \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{written}\:{and}\:{compiled}\:{by} \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\clubsuit{m}.{n}.{july}.\mathrm{1970}\clubsuit.... \\ $$
Answered by mindispower last updated on 16/Jan/21
$${is}\:{sylow}\:{theorem}\: \\ $$ $$ \\ $$