On Almost Fixed Point Free Automorphisms

Aner Shalev

doi:10.1006/jabr.1993.1100

On Almost Fixed Point Free Automorphisms

Aner Shalev^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

Ideas from the theory of p-adic analytic groups are employed in the study of finite groups having automorphisms with few fixed points. In particular we prove that the derived length of a finite p-group admitting an automorphism of order p^k with p^m fixed points is bounded in terms of p, m, k. This extends a well-known result of Alperin dealing with the case k = 1. Some applications to soluble groups are also given.

Original language	English
Pages (from-to)	271-282
Number of pages	12
Journal	Journal of Algebra
Volume	157
Issue number	1
DOIs	https://doi.org/10.1006/jabr.1993.1100
State	Published - May 1993
Externally published	Yes

Access to Document

10.1006/jabr.1993.1100

Cite this

@article{cf5780909f7e4dd8a3bdf57a833394e9,

title = "On Almost Fixed Point Free Automorphisms",

abstract = "Ideas from the theory of p-adic analytic groups are employed in the study of finite groups having automorphisms with few fixed points. In particular we prove that the derived length of a finite p-group admitting an automorphism of order pk with pm fixed points is bounded in terms of p, m, k. This extends a well-known result of Alperin dealing with the case k = 1. Some applications to soluble groups are also given.",

author = "Aner Shalev",

year = "1993",

month = may,

doi = "10.1006/jabr.1993.1100",

language = "אנגלית",

volume = "157",

pages = "271--282",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - On Almost Fixed Point Free Automorphisms

AU - Shalev, Aner

PY - 1993/5

Y1 - 1993/5

N2 - Ideas from the theory of p-adic analytic groups are employed in the study of finite groups having automorphisms with few fixed points. In particular we prove that the derived length of a finite p-group admitting an automorphism of order pk with pm fixed points is bounded in terms of p, m, k. This extends a well-known result of Alperin dealing with the case k = 1. Some applications to soluble groups are also given.

AB - Ideas from the theory of p-adic analytic groups are employed in the study of finite groups having automorphisms with few fixed points. In particular we prove that the derived length of a finite p-group admitting an automorphism of order pk with pm fixed points is bounded in terms of p, m, k. This extends a well-known result of Alperin dealing with the case k = 1. Some applications to soluble groups are also given.

UR - https://www.scopus.com/pages/publications/0001614021

U2 - 10.1006/jabr.1993.1100

DO - 10.1006/jabr.1993.1100

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0001614021

SN - 0021-8693

VL - 157

SP - 271

EP - 282

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

On Almost Fixed Point Free Automorphisms

Abstract

Access to Document

Other files and links

Fingerprint

Cite this