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- W3034287238 abstract "Abstract For a solvable group, a theorem of Gaschutz shows that <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mrow> <m:mi>F</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:mo>/</m:mo> <m:mi mathvariant=normal>Φ</m:mi> </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:math> {F(G)/Phi(G)} is a direct sum of irreducible G-modules and a faithful <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mi>G</m:mi> <m:mo>/</m:mo> <m:mi>F</m:mi> </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:math> {G/F(G)} -module. If each of these irreducible modules is primitive, we show that every non-vanishing element of G lies in <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>F</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> {F(G)} ." @default.
- W3034287238 created "2020-06-19" @default.
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- W3034287238 date "2020-06-11" @default.
- W3034287238 modified "2023-09-26" @default.
- W3034287238 title "Group actions and non-vanishing elements in solvable groups" @default.
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- W3034287238 doi "https://doi.org/10.1515/jgth-2019-0077" @default.
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