Group algebras whose groups of normalized units have exponent 4

Victor Bovdi; Mohammed Salim

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 1, page 141-148
  • ISSN: 0011-4642

Abstract

top
We give a full description of locally finite 2 -groups G such that the normalized group of units of the group algebra F G over a field F of characteristic 2 has exponent 4 .

How to cite

top

Bovdi, Victor, and Salim, Mohammed. "Group algebras whose groups of normalized units have exponent 4." Czechoslovak Mathematical Journal 68.1 (2018): 141-148. <http://eudml.org/doc/294708>.

@article{Bovdi2018,
abstract = {We give a full description of locally finite $2$-groups $G$ such that the normalized group of units of the group algebra $FG$ over a field $F$ of characteristic $2$ has exponent $4$.},
author = {Bovdi, Victor, Salim, Mohammed},
journal = {Czechoslovak Mathematical Journal},
keywords = {group of exponent 4; unit group; modular group algebra},
language = {eng},
number = {1},
pages = {141-148},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Group algebras whose groups of normalized units have exponent 4},
url = {http://eudml.org/doc/294708},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Bovdi, Victor
AU - Salim, Mohammed
TI - Group algebras whose groups of normalized units have exponent 4
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 1
SP - 141
EP - 148
AB - We give a full description of locally finite $2$-groups $G$ such that the normalized group of units of the group algebra $FG$ over a field $F$ of characteristic $2$ has exponent $4$.
LA - eng
KW - group of exponent 4; unit group; modular group algebra
UR - http://eudml.org/doc/294708
ER -

References

top
  1. Bovdi, A. A., Group Rings, University publishers, Uzgorod (1974), Russian. (1974) Zbl0339.16004MR0412282
  2. Bovdi, A., The group of units of a group algebra of characteristic p , Publ. Math. 52 (1998), 193-244. (1998) Zbl0906.16016MR1603359
  3. Bovdi, V., 10.1017/S1446788709000214, J. Aust. Math. Soc. 87 (2009), 325-328. (2009) Zbl1194.20005MR2576568DOI10.1017/S1446788709000214
  4. Bovdi, V., Dokuchaev, M., Group algebras whose involutory units commute, Algebra Colloq. 9 (2002), 49-64. (2002) Zbl1002.20003MR1883427
  5. Bovdi, V., Konovalov, A., Rossmanith, R., Schneider, C., LAGUNA Lie AlGebras and UNits of group Algebras, Version 3.5.0, 2009, http://www.cs.st-andrews.ac.uk/{alexk/laguna/}. 
  6. Bovdi, A., Lakatos, P., On the exponent of the group of normalized units of modular group algebras, Publ. Math. 42 (1993), 409-415. (1993) Zbl0802.16027MR1229688
  7. Caranti, A., 10.1016/0021-8693(85)90068-7, J. Algebra 97 (1985), 1-13. (1985) Zbl0572.20008MR0812164DOI10.1016/0021-8693(85)90068-7
  8. GAP, The GAP Group, GAP---Groups, Algorithms, and Programming, Version 4.4.12, http://www.gap-system.org. 
  9. Gupta, N. D., Newman, M. F., 10.1007/bfb0065183, Proc. 2nd Int. Conf. Theory of Groups, Canberra, 1973, Lect. Notes Math. 372, Springer, Berlin (1974), 330-332. (1974) Zbl0291.20034MR0352265DOI10.1007/bfb0065183
  10. M. Hall, Jr., The Theory of Groups, The Macmillan Company, New York (1959). (1959) Zbl0084.02202MR0103215
  11. Janko, Z., 10.1016/j.jalgebra.2007.02.010, J. Algebra 315 (2007), 801-808. (2007) Zbl1127.20018MR2351894DOI10.1016/j.jalgebra.2007.02.010
  12. Janko, Z., 10.1016/j.jalgebra.2009.03.004, J. Algebra 321 (2009), 2890-2897. (2009) Zbl1177.20031MR2512633DOI10.1016/j.jalgebra.2009.03.004
  13. Janko, Z., 10.1016/j.jalgebra.2014.05.027, J. Algebra 416 (2014), 274-286. (2014) Zbl1323.20016MR3232801DOI10.1016/j.jalgebra.2014.05.027
  14. Quick, M., 10.1112/S0024610799008169, J. Lond. Math. Soc., II. Ser. 60 (1999), 747-756. (1999) Zbl0955.20014MR1753811DOI10.1112/S0024610799008169
  15. Shalev, A., 10.1016/0021-8693(90)90228-G, J. Algebra 129 (1990), 412-438. (1990) Zbl0695.16007MR1040946DOI10.1016/0021-8693(90)90228-G
  16. Shalev, A., 10.1112/jlms/s2-43.1.23, J. Lond. Math. Soc., II. Ser. 43 (1991), 23-36. (1991) Zbl0669.16005MR1099083DOI10.1112/jlms/s2-43.1.23
  17. Vaughan-Lee, M. R., Wiegold, J., 10.1112/blms/13.1.45, Bull. Lond. Math. Soc. 13 (1981), 45-46. (1981) Zbl0418.20027MR0599640DOI10.1112/blms/13.1.45

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.