【摘要】 若对群G中任意子群(阿贝尔子群或循环子群)H有|HG∶H|<∞,则称群G是S(A,C)群.若|HG∶H|≤n,则称群G是S(n)(A(n),C(n))群.在有限p群条件下,对偶研究S(A,C)群,证明了C(p)p群的幂零类不超过3,其导群是初等阿贝尔群.更多还原

【Abstract】 Let G be a group, one says that G is an S~*(A~*, C~*)-group, if each(abelian, or cyclic)subgroup H of G satisfies that ｜H~G∶H｜<∞; further, one says that G is an S~*(n)(A~*(n), C~*(n))-group, if each(abelian, or cyclic)subgroup H of G satisfies that ｜H~G∶H｜≤n. In this paper, by investigating finite C~*(p)-p-groups the authors have obtained that the nilpotent class of C~*(p)-p-groups is at most 3 and their derived subgroup is elementary abelian p-group.更多还原