On integrated screens

Author:
J. C. Beidleman

Journal:
Proc. Amer. Math. Soc. **42** (1974), 36-38

MSC:
Primary 20D10

MathSciNet review:
0327891

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Abstract: Let be a screen with support and let denote the saturated formation of finite solvable groups which is locally induced by . For each prime *p*, let . Then is an integrated screen which locally induces and . The purpose of this note is to prove the following theorems. Theorem 1. *Assume that for each finite solvable group G the* -*izers of G satisfy the strict cover-avoidance property. Then* *is an integrated screen*; *that is* *for each prime p*. Theorem 2. *Assume that for each group G an* -*izer of an* -*izer of G is an* -*izer of G. Then* *for each prime p*.

**[1]**Roger Carter and Trevor Hawkes,*The \cal𝐹-normalizers of a finite soluble group*, J. Algebra**5**(1967), 175–202. MR**0206089****[2]**Klaus Doerk,*Zur Theorie der Formationen endlicher auflösbarer Gruppen*, J. Algebra**13**(1969), 345–373 (German). MR**0246968****[3]**Gary M. Seitz and C. R. B. Wright,*On complements of 𝔉-residuals in finite solvable groups*, Arch. Math. (Basel)**21**(1970), 139–150. MR**0271234****[4]**Charles R. B. Wright,*On screens of 𝔏-izers of finite solvable groups*, Math. Z.**115**(1970), 273–282. MR**0262365**

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DOI:
https://doi.org/10.1090/S0002-9939-1974-0327891-1

Keywords:
Screen,
formation,
-izer,
solvable

Article copyright:
© Copyright 1974
American Mathematical Society