p-constrained group

<h2 id="definition">Definition</h2>
If a group has trivial p′ <a href="/facts/Core_(group_theory)/IGEJE92q">core</a> Op′(G), then it is defined to be p-constrained if the p-core Op(G) contains its centralizer, or in other words if its <a href="/facts/Generalized_Fitting_subgroup/EIXK0ANT">generalized Fitting subgroup</a> is a p-group. More generally, if Op′(G) is non-trivial, then G is called p-constrained if G/Op′(G) is p-constrained.
All <a href="/facts/P-solvable_group/IGEJE92q">p-solvable groups</a> are p-constrained.

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/P-stable_group/MXVJNzUz">p-stable group</a></li>
<li>The <a href="/facts/ZJ_theorem/DQYRweox">ZJ theorem</a> has p-constraint as one of its conditions.</li></ul>

<ul><li><a href="/facts/Daniel_Gorenstein/tBgFlDpt">Gorenstein, D.</a>; Walter, John H. (1964), "On the maximal subgroups of finite simple groups", <a href="/facts/Journal_of_Algebra/Xr6PbIKM">Journal of Algebra</a>, 1 (2): 168–213, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2F0021-8693%2864%2990032-8">10.1016/0021-8693(64)90032-8</a>, <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0021-8693">0021-8693</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0172917">0172917</a></li>
<li><a href="/facts/Daniel_Gorenstein/tBgFlDpt">Gorenstein, D.</a> (1980), <a href="https://www.ams.org/bookstore-getitem/item=CHEL-301-H">Finite groups</a> (2nd ed.), New York: Chelsea Publishing Co., <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-8284-0301-6, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0569209">0569209</a></li></ul>

p-constrained group open-in-new

p-constrained group