Artinian automorphisms of infinite groups

Antonella Leone

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 575-582
  • ISSN: 0392-4033

Abstract

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An automorphism a of a group G is called an artinian automorphism if for every strictly descending chain H 1 > H 2 > > H n > of subgroups of G there exists a positive integer m such that ( H n ) a = H n for every n m . In this paper we show that in many cases the group of all artinian automorphisms of G coincides with the group of all power automorphisms of G .

How to cite

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Leone, Antonella. "Artinian automorphisms of infinite groups." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 575-582. <http://eudml.org/doc/289638>.

@article{Leone2006,
abstract = {An automorphism a of a group G is called an artinian automorphism if for every strictly descending chain $H_1 > H_2 > \cdots > H_n > \cdots$ of subgroups of G there exists a positive integer $m$ such that $(H_n)^a = H_n$ for every $n \geq m$. In this paper we show that in many cases the group of all artinian automorphisms of $G$ coincides with the group of all power automorphisms of $G$.},
author = {Leone, Antonella},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {575-582},
publisher = {Unione Matematica Italiana},
title = {Artinian automorphisms of infinite groups},
url = {http://eudml.org/doc/289638},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Leone, Antonella
TI - Artinian automorphisms of infinite groups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 575
EP - 582
AB - An automorphism a of a group G is called an artinian automorphism if for every strictly descending chain $H_1 > H_2 > \cdots > H_n > \cdots$ of subgroups of G there exists a positive integer $m$ such that $(H_n)^a = H_n$ for every $n \geq m$. In this paper we show that in many cases the group of all artinian automorphisms of $G$ coincides with the group of all power automorphisms of $G$.
LA - eng
UR - http://eudml.org/doc/289638
ER -

References

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  1. BEIDLEMAN, J. C. - HEINEKEN, H., A note on I-Automorphisms, J. Algebra, 234 (2000), 694-706. Zbl0976.20022
  2. COOPER, C. D. H., Power automorphisms of a group, Math. Z., 107 (1968), 335-356. Zbl0169.33801
  3. CURZIO, M. - FRANCIOSI, S. - DE GIOVANNI, F., On automorphisms fixing infinite subgroups of groups, Arch. Math.54 (1990), 4-13. Zbl0664.20018
  4. HARTLEY, B., Fixed points of automorphisms of certain locally finite groups and Chevalley groups, J. London Math. Soc. (2), 37 (1988), 421-436. Zbl0619.20018
  5. PHILLIPS, R. E. - WILSON, J. S., On certain minimal conditions for infinite groups, J. Algebra, 51 (1978), 41-68. Zbl0374.20042
  6. ROBINSON, D. J. S., Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin, 1972. Zbl0243.20032
  7. ŠUNKOV, V. P., On the minimality problem for locally finite groups, Algebra and Logic, 9 (1970), 137-151. 
  8. ZAICEV, D. I., On solvable subgroups of locally solvable groups, Soviet. Math. Dokl., 15 (1974), 342-345. Zbl0322.20017

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