数学进展
數學進展
수학진전
ADVANCES IN MATHEMATICS
2008年
4期
494-498
,共5页
超特殊p-群%中心积%特征子群
超特殊p-群%中心積%特徵子群
초특수p-군%중심적%특정자군
superspecial p-groups%central product%characteristic subgroup
本文获得了以下结果:设G为有限超特殊P-群.则下列条件等价: (1)G的非平凡特征子群的阶相同; (2)G的非平凡特征子群唯一; (3)当P＞2时,expG=p;当P=2时,G≠D8.
本文穫得瞭以下結果:設G為有限超特殊P-群.則下列條件等價: (1)G的非平凡特徵子群的階相同; (2)G的非平凡特徵子群唯一; (3)噹P＞2時,expG=p;噹P=2時,G≠D8.
본문획득료이하결과:설G위유한초특수P-군.칙하렬조건등개: (1)G적비평범특정자군적계상동; (2)G적비평범특정자군유일; (3)당P＞2시,expG=p;당P=2시,G≠D8.
In this paper, we studied finite p-groups all of whose nontriviai characteristic sub-groups have the same order. We get that if G is a finite superspeciai p-group, then the following conditions are equivalent: (1) Nontriviai characteristic subgroups of G have the same order; (2) G has unique nontriviai characteristic subgroup; (3) If p ＞ 2, exp G = p, if p=2, G≠Ds.
