On integrated screens

Author:
J. C. Beidleman

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

MSC:
Primary 20D10

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

MathSciNet review:
0327891

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Abstract | References | Similar Articles | Additional Information

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]**R. Carter and T. Hawkes,*The*-*normalizer of a finite soluble group*, J. Algebra**5**(1967), 175-202. MR**34**#5914. MR**0206089 (34:5914)****[2]**K. Doerk,*Zur Theorie der Formationen endlicher auflösbarer Gruppen*, J. Algebra**13**(1969), 345-373. MR**40**#237. MR**0246968 (40:237)****[3]**G. Seitz and C. Wright,*On complements of*-*residuals in finite solvable groups*, Arch. Math. (Basel)**21**(1970), 139-150. MR**42**#6117. MR**0271234 (42:6117)****[4]**C. Wright,*On screens and*-*izers of finite solvable groups*, Math. Z.**115**(1970), 273-282. MR**41**#6973. MR**0262365 (41:6973)**

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Additional Information

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

Keywords:
Screen,
formation,
-izer,
solvable

Article copyright:
© Copyright 1974
American Mathematical Society