Let
G be a finite group not of prime power order. A gap
G-module
V is a finite-dimensional real
G-representation space satisfying the following two conditions. The first is the condition dim
VP > 2 dim
VH for all
P <
H ≤
G such that
P is of prime power order and the other is the condition that
V has only one
H-fixed point 0 for all large subgroups
H : precisely to say,
H ∈
L(
G). If there exists a gap
G-module, then
G is called a gap group. We study
G-modules induced from
C-modules for subgroups
C of
G and obtain a sufficient condition for
G to become a gap group. Consequently, we show that non-solvable general linear groups and the automorphism groups of sporadic groups are all gap groups.
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