Search

Let G be a finite group and H ≤ G. The authors study the structure of finite groups G having a subgroup H which is maximal in 〈H, Hg〉 for some g ∈ G. Some results on the structure of 〈H, Hg〉 and G are set up. Especially, a generalization of Baer′s theorem is established.

This study focuses on using the chemical compositions of plagioclase to further investigate the petrogenesis of Chang'E-5 young mare basalts and constrain its parental melt composition. Together with previously published data, our results show that the plagioclase in mare basalts overall displays large variations in major and trace element concentrations. Inversion of the plagioclase data indicates that the melt compositions parental to Chang'E-5 basalts have high rare earth elements (REE) concentrations similar to the high-K KREEP rocks (potassium, rare earth elements, and phosphorus). Such a signature is unlikely to result from the assimilation of KREEP components, because the estimated melt Sr shows positive correlations with other trace elements (e.g., Ba, La), which are far from the KREEP end-member. Instead, the nearly parallel REE distributions and a high degree of trace element enrichment in plagioclase indicate an extensive fractional crystallization process. Furthermore, the estimated melt REE concentrations from plagioclase are slightly higher than those from clinopyroxene, consistent with its relatively later crystallization. Using the Ti partition coefficient between plagioclase and melt, we estimated the parental melt TiO2 content from the earliest crystallized plagioclase to be ~3.3 ± 0.4 wt%, thus providing robust evidence for a low-Ti and non-KREEP origin for the Chang'E-5 young basalts in the Procellarum KREEP terrane. [ABSTRACT FROM AUTHOR]

We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.

In this paper, we classify the -groups all of whose proper subgroups have cyclic Frattini subgroups, for an odd prime . [ABSTRACT FROM AUTHOR]