Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
group of exponent 4; unit group; modular group algebra
group of exponent 4; unit group; modular group algebra
Summary:
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 $4$.
References:
[1] Bovdi, A. A.: Group Rings. University publishers, Uzgorod (1974), Russian. MR 0412282 | Zbl 0339.16004
[2] Bovdi, A.: The group of units of a group algebra of characteristic $p$. Publ. Math. 52 (1998), 193-244. MR 1603359 | Zbl 0906.16016
[3] Bovdi, V.: Group algebras whose group of units is powerful. J. Aust. Math. Soc. 87 (2009), 325-328. DOI 10.1017/S1446788709000214 | MR 2576568 | Zbl 1194.20005
[4] Bovdi, V., Dokuchaev, M.: Group algebras whose involutory units commute. Algebra Colloq. 9 (2002), 49-64. MR 1883427 | Zbl 1002.20003
[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. MR 1229688 | Zbl 0802.16027
[7] Caranti, A.: Finite $p$-groups of exponent $p^2$ in which each element commutes with its endomorphic images. J. Algebra 97 (1985), 1-13. DOI 10.1016/0021-8693(85)90068-7 | MR 0812164 | Zbl 0572.20008
[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.: The nilpotency class of finitely generated groups of exponent four. Proc. 2nd Int. Conf. Theory of Groups, Canberra, 1973, Lect. Notes Math. 372, Springer, Berlin (1974), 330-332. DOI 10.1007/bfb0065183 | MR 0352265 | Zbl 0291.20034
[10] M. Hall, Jr.: The Theory of Groups. The Macmillan Company, New York (1959). MR 0103215 | Zbl 0084.02202
[11] Janko, Z.: On finite nonabelian 2-groups all of whose minimal nonabelian subgroups are of exponent 4. J. Algebra 315 (2007), 801-808. DOI 10.1016/j.jalgebra.2007.02.010 | MR 2351894 | Zbl 1127.20018
[12] Janko, Z.: Finite nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent 4. J. Algebra 321 (2009), 2890-2897. DOI 10.1016/j.jalgebra.2009.03.004 | MR 2512633 | Zbl 1177.20031
[13] Janko, Z.: Finite $p$-groups of exponent $p^e$ all of whose cyclic subgroups of order $p^e$ are normal. J. Algebra 416 (2014), 274-286. DOI 10.1016/j.jalgebra.2014.05.027 | MR 3232801 | Zbl 1323.20016
[14] Quick, M.: Varieties of groups of exponent 4. J. Lond. Math. Soc., II. Ser. 60 (1999), 747-756. DOI 10.1112/S0024610799008169 | MR 1753811 | Zbl 0955.20014
[15] Shalev, A.: Dimension subgroups, nilpotency indices, and the number of generators of ideals in $p$-group algebras. J. Algebra 129 (1990), 412-438. DOI 10.1016/0021-8693(90)90228-G | MR 1040946 | Zbl 0695.16007
[16] Shalev, A.: Lie dimension subgroups, Lie nilpotency indices, and the exponent of the group of normalized units. J. Lond. Math. Soc., II. Ser. 43 (1991), 23-36. DOI 10.1112/jlms/s2-43.1.23 | MR 1099083 | Zbl 0669.16005
[17] Vaughan-Lee, M. R., Wiegold, J.: Countable locally nilpotent groups of finite exponent without maximal subgroups. Bull. Lond. Math. Soc. 13 (1981), 45-46. DOI 10.1112/blms/13.1.45 | MR 0599640 | Zbl 0418.20027
Search
Partner of
