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- W2904698728 abstract "Abstract Let H be a nilpotent subgroup of a finite nonabelian group G , let <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>π</m:mi> <m:mo>=</m:mo> <m:mrow> <m:mi>π</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo stretchy=false>|</m:mo> <m:mi>H</m:mi> <m:mo stretchy=false>|</m:mo> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {pi=pi(|H|)} and let <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>bcl</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>G</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {{operatorname{bcl}}(G)} be the largest conjugacy class size of the group G . In the present paper, we show that <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mo stretchy=false>|</m:mo> <m:mrow> <m:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo></m:mo> <m:msub> <m:mi>O</m:mi> <m:mi>π</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>G</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo>/</m:mo> <m:msub> <m:mi>O</m:mi> <m:mi>π</m:mi> </m:msub> </m:mrow> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>G</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy=false>|</m:mo> </m:mrow> <m:mo><</m:mo> <m:mrow> <m:mi>bcl</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>G</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {|HO_{pi}(G)/O_{pi}(G)|<{operatorname{bcl}}(G)} ." @default.
- W2904698728 created "2018-12-22" @default.
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- W2904698728 date "2018-12-06" @default.
- W2904698728 modified "2023-10-17" @default.
- W2904698728 title "The largest conjugacy class size and the nilpotent subgroups of finite groups" @default.
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- W2904698728 doi "https://doi.org/10.1515/jgth-2018-0040" @default.
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