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- W4243301956 abstract "Let $lambda$ be a linear character on the center Z of a finite group Z of a finite group H, such that (1) ${lambda ^H} = sum nolimits _{i = 1}^p {{phi _i}(1){phi _i}}$ where the ${phi _i}$âs are inequivalent irreducible characters on H of the same degree, and (2) if $sum nolimits _{i = 1}^p {{m_i}{phi _i}(x) = 0}$ for some $x in H$ and nonnegative integers ${m_i}$, then either ${phi _i}(x) = 0$ for all i or ${m_i} = {m_j}$ for all i, j. The object of the paper is to describe finite groups which satisfy conditions (1) and (2) in terms of the multiplication of the group. If S is a p Sylow subgroup of the group H, and $R = S cdot Z$, then H satisfies conditions (1) and (2) if and only if (a) ${ x in H:{x^{ - 1}}{h^{ - 1}}xh in Z Rightarrow lambda ({x^{ - 1}}{h^{ - 1}}xh) = 1,h in H} /Z$ consists of elements of order a power of p in $H/Z$, and these elements form p conjugacy classes of $H/Z$, and (b) the elements of ${ x in R:{x^{ - 1}}{r^{ - 1}}xr in Z Rightarrow lambda ({x^{ - 1}}{r^{ - 1}}xr) = 1,r in R} /Z$ form p conjugacy classes of $R/Z$." @default.
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- W4243301956 date "1974-03-01" @default.
- W4243301956 modified "2023-10-16" @default.
- W4243301956 title "Subgroups of Groups of Central Type" @default.
- W4243301956 doi "https://doi.org/10.2307/1996851" @default.
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