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تشخيصپذيري و k- تشخيصپذيري بعضي از گروههاي متناهي با استفاده از دو روش، مجموعه تعداد عناصر هم مرتبه و تعداد سيلو زيرگروههاي يك گروه با مركز بديهي
تعداد 82صفحه در فایل word
دكتري رشته رياضي محض (Ph.D)
تشخيصپذيري و k- تشخيصپذيري بعضي از گروههاي متناهي با استفاده از دو روش، مجموعه تعداد عناصر هم مرتبه و تعداد سيلو زيرگروههاي يك گروه با مركز بديهي
چكيده
فرض كنيد G يك گروه باشد اگر مجموعه تمام مرتبه های عناصرگروه G را با نماد نشان دهیم آنگاه مجموعه تمام عناصر هم مرتبه G را که با نماد nse(G) نمایش می دهند به صورت تعریف می کنند. در اين رساله ابتدا نشان ميدهيم اگر جائيكه S گروه متناوب ساده ، يا گروههاي خطي طوري كه يا گروههاي متقارن طوري كه و يا گروههاي ساده ماتيو آنگاه G با S ايزومورف است. همچنين نشان ميدهيم اگر G گروهي متناهي با مركز بديهي باشد طوري كه تعداد سيلو زيرگروههاي آن به ازاي هر عدد اول با تعداد سيلو زيرگروههاي گروهاي خطي كه درآن برابر باشد آنگاه G بايد در شرط صدق كند.
تشخيصپذيري و k- تشخيصپذيري بعضي از گروههاي متناهي با استفاده از دو روش، مجموعه تعداد عناصر هم مرتبه و تعداد سيلو زيرگروههاي يك گروه با مركز بديهي
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