Abstract
AbstractLet G be a finite group, N a normal subgroup of G and K a conjugacy class of G. We prove that if $$K\cup K^{-1}$$
K
∪
K
-
1
is union of cosets of N, then N is soluble, K is a real-imaginary class, that is, every irreducible character of G takes real or purely imaginary values on K, and if, in addition, the elements of K are p-elements for some prime p, then N has normal p-complement. We also prove that if $$K\cup K^{-1}$$
K
∪
K
-
1
is a single coset of N, then $$\langle K\rangle $$
⟨
K
⟩
has a normal 2-complement.
Publisher
Springer Science and Business Media LLC
Cited by
2 articles.
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