A note on an “Anzahl” theorem of P. Hall

2019 ◽  
Vol 19 (09) ◽  
pp. 2050163
Author(s):  
Boyan Wei ◽  
Haipeng Qu ◽  
Yanfeng Luo
Keyword(s):  
Index Formula ◽  
Frattini Subgroup

Let [Formula: see text] be a prime and [Formula: see text] a finite [Formula: see text]-group. Hall proved [Formula: see text] for [Formula: see text], where [Formula: see text] is the number of subgroups of index [Formula: see text] which do not contain the Frattini subgroup of [Formula: see text]. We determine the minimal values of [Formula: see text] for [Formula: see text] and [Formula: see text].

Index Formula Index

1989 ◽  
Author(s):  
Rainer Bohrer ◽  
Helga Hartwig ◽  
Renate Jonuschat ◽  
Bernd Kalbskopf ◽  
Renate Nohl ◽  
...  
Keyword(s):  
Index Formula

scholarly journals Bounds in groups with trivial Frattini subgroup

2008 ◽  
Vol 319 (3) ◽  
pp. 893-896 ◽  
Author(s):  
Z. Halasi ◽  
K. Podoski
Keyword(s):  
Frattini Subgroup

Developing an Outsourcing Partner Selection Model for Process with Two-Sided Specification Using Capability Index and Manufacturing Time Performance Index

2019 ◽  
Vol 26 (03) ◽  
pp. 1950015 ◽  
Author(s):  
Kuen-Suan Chen ◽  
Tsang-Chuan Chang ◽  
Yun-Tsan Lin
Keyword(s):  
Performance Index ◽  
Business Models ◽  
Partner Selection ◽  
Selection Model ◽  
Index Formula ◽  
Time Performance ◽  
Capability Index ◽  
Point Estimates ◽  
Manufacturing Time

In the face of fierce global competition, firms are outsourcing important but nonessential tasks to external professional companies. Corporations are also turning from competitive business models to cooperative strategic partnerships in hopes of swiftly responding to consumer needs and enhancing overall efficiency and industry competitiveness. This research developed an outsourcing partner selection model in hopes of helping firms select better outsourcing partners for long-term collaborations. Process quality and manufacturing time are vital when evaluating outsourcing partner. We therefore used process capability index [Formula: see text] and manufacturing time performance index [Formula: see text] in the proposed model. Sample data from random samples are needed to calculate the point estimates of indices, however, it is impossible to obtain a sample with a structure completely identical to that of the population, which means that sampling generates unavoidable sampling errors. The reliability of point estimates are also uncertain, which inevitably leads to misjudgment in some cases. Thus, to reduce estimate errors and increase assessment reliability, we calculated the [Formula: see text]% confidence intervals of the indices [Formula: see text] and [Formula: see text], then constructed the joint confidence region of [Formula: see text] and [Formula: see text] to develop an outsourcing partner selection model that will help firms select better outsourcing partners for long-term collaborations. We also provide a case as an illustration of how the proposed selection model is implemented.

scholarly journals A generalized Frattini subgroup of a finite group

1989 ◽  
Vol 12 (2) ◽  
pp. 263-266
Author(s):  
Prabir Bhattacharya ◽  
N. P. Mukherjee
Keyword(s):  
Finite Group ◽  
Maximal Subgroups ◽  
Frattini Subgroup ◽  
Definition Of ◽  
A Finite Group

For a finite group G and an arbitrary prime p, letSP(G)denote the intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we setSP(G)= G. Some properties of G are considered involvingSP(G). In particular, we obtain a characterization of G when each M in the definition ofSP(G)is nilpotent.

Addendum to "On the Frattini Subgroup"

1971 ◽  
Vol 27 (1) ◽  
pp. 63
Author(s):  
John Cossey ◽  
Alice Whittemore
Keyword(s):  
Frattini Subgroup
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