On solvable groups whose Sylow subgroups are either abelian or extraspecial
Trudy Instituta matematiki, Tome 20 (2012) no. 2, pp. 3-9
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A $p$-group $G$ is called extraspecial if its derived subgroup, center and Frattini subgroup are groups of order $p.$ We consider the solvable groups whose Sylow subgroups are either abelian or extraspecial. It is proved that derived length is at most $2\cdot|\pi(G)|$ and nilpotent length is at most $2+|\pi(G)|$.
@article{TIMB_2012_20_2_a0,
author = {D. V. Gritsuk and V. S. Monakhov},
title = {On solvable groups whose {Sylow} subgroups are either abelian or extraspecial},
journal = {Trudy Instituta matematiki},
pages = {3--9},
publisher = {mathdoc},
volume = {20},
number = {2},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMB_2012_20_2_a0/}
}
TY - JOUR AU - D. V. Gritsuk AU - V. S. Monakhov TI - On solvable groups whose Sylow subgroups are either abelian or extraspecial JO - Trudy Instituta matematiki PY - 2012 SP - 3 EP - 9 VL - 20 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMB_2012_20_2_a0/ LA - ru ID - TIMB_2012_20_2_a0 ER -
D. V. Gritsuk; V. S. Monakhov. On solvable groups whose Sylow subgroups are either abelian or extraspecial. Trudy Instituta matematiki, Tome 20 (2012) no. 2, pp. 3-9. http://geodesic.mathdoc.fr/item/TIMB_2012_20_2_a0/