Groups of order p^۸ and exponent p
عنوان مقاله: Groups of order p^۸ and exponent p
شناسه ملی مقاله: JR_THEGR-4-4_002
منتشر شده در در سال 1394
شناسه ملی مقاله: JR_THEGR-4-4_002
منتشر شده در در سال 1394
مشخصات نویسندگان مقاله:
Michael Vaughan-Lee - Oxford University Mathematical Institute
خلاصه مقاله:
Michael Vaughan-Lee - Oxford University Mathematical Institute
We prove that for p>۷ there are \[ p^{۴}+۲p^{۳}+۲۰p^{۲}+۱۴۷p+(۳p+۲۹)\gcd (p-۱,۳)+۵\gcd (p-۱,۴)+۱۲۴۶ \] groups of order p^{۸} with exponent p. If P is a group of order p^{۸} and exponent p, and if P has class c>۱ then P is a descendant of P/\gamma _{c}(P). For each group of exponent p with order less than p^{۸} we calculate the number of descendants of order p^{۸} with exponent p. In all but one case we are able to obtain a complete and irredundant list of the descendants. But in the case of the three generator class two group of order p^{۶} and exponent p (p>۳), while we are able to calculate the number of descendants of order p^{۸}, we have not been able to obtain a list of the descendants.
کلمات کلیدی: Groups of exponent p, Groups of order p^۸, PORC conjecture
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1199647/