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- W2963474543 abstract "Abstract Denote by <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>ν</m:mi> <m:mi>p</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:math> {nu_{p}(G)} the number of Sylow p -subgroups of G . It is not difficult to see that <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:msub> <m:mi>ν</m:mi> <m:mi>p</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>H</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo>⩽</m:mo> <m:mrow> <m:msub> <m:mi>ν</m:mi> <m:mi>p</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:mrow> </m:math> {nu_{p}(H)leqslantnu_{p}(G)} for <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>H</m:mi> <m:mo>⩽</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> {Hleqslant G} , however <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>ν</m:mi> <m:mi>p</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>H</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {nu_{p}(H)} does not divide <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>ν</m:mi> <m:mi>p</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:math> {nu_{p}(G)} in general. In this paper we reduce the question whether <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>ν</m:mi> <m:mi>p</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>H</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {nu_{p}(H)} divides <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>ν</m:mi> <m:mi>p</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:math> {nu_{p}(G)} for every <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>H</m:mi> <m:mo>⩽</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> {Hleqslant G} to almost simple groups. This result substantially generalizes the previous result by G. Navarro and also provides an alternative proof of Navarro’s theorem." @default.
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- W2963474543 date "2018-04-17" @default.
- W2963474543 modified "2023-09-22" @default.
- W2963474543 title "Number of Sylow subgroups in finite groups" @default.
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- W2963474543 doi "https://doi.org/10.1515/jgth-2018-0010" @default.
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