Elements of order at most 4 in finite 2-groups
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| 024 | 7 | 0 | |a 10.1515/jgth.2004.7.4.431 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/jgth.2004.7.4.431 | ||
| 100 | 1 | |a Janko |D Zvonimir | |
| 245 | 1 | 0 | |a Elements of order at most 4 in finite 2-groups |h [Elektronische Daten] |c [Zvonimir Janko] |
| 520 | 3 | |a 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. | |
| 540 | |a © de Gruyter | ||
| 690 | 7 | |a Mathematical foundations |2 nationallicence | |
| 690 | 7 | |a Applied mathematics |2 nationallicence | |
| 690 | 7 | |a Number theory |2 nationallicence | |
| 773 | 0 | |t Journal of Group Theory |d Walter de Gruyter |g 7/4(2004-09-06), 431-436 |x 1433-5883 |q 7:4<431 |1 2004 |2 7 |o jgth | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/jgth.2004.7.4.431 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/jgth.2004.7.4.431 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Janko |D Zvonimir | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Group Theory |d Walter de Gruyter |g 7/4(2004-09-06), 431-436 |x 1433-5883 |q 7:4<431 |1 2004 |2 7 |o jgth | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
| 986 | |a SWISSBIB |b 378894595 | ||
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||