<prompt> Bheka isigaba esingezansi bese uphendula umbuzo emva kwalokho ngolimi olufanayo nesigaba: Isendlalelo: Izazi zezibalo zivame ukulwela ukuhlukanisa ngokuphelele noma uhlu lomqondo wezibalo. Ngokuphathelene namaqembu aphelele, lo mgomo uholela ezifundweni eziyinkimbinkimbi. Ngokusho kwe Lagranges theorem, amaqembu aphelele ohlelo p, inombolo yokuqala, ngokuyisisekelo amaqembu ajikelezayo ka-Abelian Zp. Amaqembu e-order p2 nawo angaboniswa ukuthi angama-Abelian, isitatimende esingajwayelekile ku-order p3, njengoba iqembu elingeyona i-Abelian D4 le-order 8 23 ngenhla likhombisa. Izinhlelo ze-computer ze-algebra zingasetshenziselwa ukufaka uhlu lwamaqembu amancane, kodwa akukho ukuhlukaniswa kwawo wonke amaqembu aphelele. Isinyathelo esiphakathi ukuhlukaniswa kwamaqembu alula aphelele. Iqembu elingasho lutho libizwa ngokuthi lilula uma amaqembu alo amancane avamile kuyiqembu elingasho lutho neqembu ngokwalo. I-Jordan-Hölder theorem ibonisa amaqembu alula aphelele njengamabhulokhi okwakha wonke amaqembu aphelele. Ukwenza uhlu lwawo wonke amaqembu alula aphelele kwakuyimpumelelo enkulu emfundisweni yeqembu yesimanje. Ngo-1998 umnqobi we-Fields Medal uRichard Borcherds waphumelela ekufakazeleni izinganekwane ze-monstrous moonshine, ubudlelwano obumangalisayo nobujulile phakathi kweqembu elikhulu elilinganiselwe elilula kakhulu - iqembu le-monster - nemisebenzi ethile ye-modular, ucezu lokuhlaziya okuyinkimbinkimbi yakudala, kanye nemfundiso ye-string, inkolelo-mbono okuthiwa ihlanganisa incazelo yezenzakalo eziningi zomzimba. Umbuzo: Yini eyabhekwa njengempumelelo enkulu kuyi-theorem kaJordan-Holder?  <response>: Uhlu lwawo wonke amaqembu alula aphelele 