caa a22 4500 378894595 CHVBK 20180305123503.0 cr unu---uuuuu 161128e20040906xx s 000 0 eng 10.1515/jgth.2004.7.4.431 doi (NATIONALLICENCE)gruyter-10.1515/jgth.2004.7.4.431 Janko Zvonimir Elements of order at most 4 in finite 2-groups [Elektronische Daten] [Zvonimir Janko] It is a known fact that the subgroup Ω2(G) generated by all elements of order at most 4 in a finite 2-group G has a strong influence on the structure of the whole group G. For example, if Ω2(G) is metacyclic, then G is also metacyclic (N. Blackburn). Here we consider the case Ω2(G) = C 2 x D, where C 2 is cyclic of order 2 and D is any 2-group of maximal class and we show that ❘G : Ω2(G)❘ ≤ 2 and the structure of G is uniquely determined. We determine also the structure of a finite 2-group G whose elements of order 4 generate the subgroup Ω* 2 (G) ≅ C 2 × Q 2 n , where Q 2 n is generalized quaternion of order 2 n . Finally, we show that a finite p-group G all of whose non-cyclic subgroups are generated by elements of order p is cyclic or of exponent p or a dihedral 2-group. © de Gruyter Mathematical foundations nationallicence Applied mathematics nationallicence Number theory nationallicence Journal of Group Theory Walter de Gruyter 7/4(2004-09-06), 431-436 1433-5883 7:4<431 2004 7 jgth https://doi.org/10.1515/jgth.2004.7.4.431 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/jgth.2004.7.4.431 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Janko Zvonimir NATIONALLICENCE 773 0- Journal of Group Theory Walter de Gruyter 7/4(2004-09-06), 431-436 1433-5883 7:4<431 2004 7 jgth CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence SWISSBIB 378894595 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter