| Title:
             | 
Inert subgroups of uncountable locally finite groups (English) | 
| Author:
             | 
Majcher-Iwanow, Barbara | 
| Language:
             | 
English | 
| Journal:
             | 
Commentationes Mathematicae Universitatis Carolinae | 
| ISSN:
             | 
0010-2628 (print) | 
| ISSN:
             | 
1213-7243 (online) | 
| Volume:
             | 
44 | 
| Issue:
             | 
4 | 
| Year:
             | 
2003 | 
| Pages:
             | 
615-622 | 
| . | 
| Category:
             | 
math | 
| . | 
| Summary:
             | 
Let $G$ be an uncountable universal locally finite group. We study subgroups $H<G$ such that for every $g\in G$, $|H:H\cap H^g|<|H|$. (English) | 
| Keyword:
             | 
universal locally finite group | 
| Keyword:
             | 
inert subgroup | 
| MSC:
             | 
20A15 | 
| MSC:
             | 
20E07 | 
| MSC:
             | 
20E25 | 
| MSC:
             | 
20F50 | 
| idZBL:
             | 
Zbl 1101.20023 | 
| idMR:
             | 
MR2062877 | 
| . | 
| Date available:
             | 
2009-01-08T19:31:33Z | 
| Last updated:
             | 
2012-04-30 | 
| Stable URL:
             | 
http://hdl.handle.net/10338.dmlcz/119415 | 
| . | 
| Reference:
             | 
[1] Belyaev V.: Locally finite groups with a finite non-separated subgroups.Siberian Math. J. 34 (1993), 2 23-39. MR 1223752 | 
| Reference:
             | 
[2] Hall Ph.: Some constructions for locally finite groups.J. London Math. Soc. 34 (1959), 305-319. Zbl 0088.02301, MR 0162845 | 
| Reference:
             | 
[3] Hickin K.: Universal locally finite central extensions of groups.Proc. London Math. Soc. 52 (1986), 53-72. Zbl 0582.20022, MR 0812445 | 
| Reference:
             | 
[4] Kegel O., Wehrfritz B.: Locally Finite Groups.North-Holland, Amsterdam, 1973. Zbl 0259.20001, MR 0470081 | 
| Reference:
             | 
[5] Keisler H.J.: Model Theory for Infinitary Logic.North-Holland, Amsterdam, 1971. Zbl 0222.02064 | 
| Reference:
             | 
[6] Macintyre A., Shelah S.: Uncountable universal locally finite groups.J. Algebra 43 (1976), 168-175. Zbl 0363.20032, MR 0439625 | 
| Reference:
             | 
[7] Mekler A.: On residual properties.Proc. Amer. Math. Soc. 78 (1980), 187-188. Zbl 0448.03021, MR 0550490 | 
| Reference:
             | 
[8] Morley M.: Homogeneous sets.in: Handbook of Mathematical Logic, edited by J. Barwise, North-Holland, Amsterdam, 1977, pp.181-196. MR 0457132 | 
| . |