On intersections of two non-incident subgroups of finite <i>p</i>-groups
On intersections of two non-incident subgroups of finite <i>p</i>-groups
Abstract In this paper, we investigate finite p -groups <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>G</m:mi> </m:math> G such that whenever <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>A</m:mi> <m:mo>,</m:mo> <m:mi>B</m:mi> <m:mo><</m:mo> <m:mi>G</m:mi> </m:math> A,B\lt G are non-incident, then <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>A</m:mi> <m:mo>∩</m:mo> <m:mi>B</m:mi> <m:mspace width="0.33em" /> <m:mo>⊴</m:mo> <m:mspace width="0.33em" /> <m:mrow> <m:mo>⟨</m:mo> <m:mrow> <m:mi>A</m:mi> <m:mo>,</m:mo> <m:mi>B</m:mi> </m:mrow> <m:mo>⟩</m:mo> …