Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 64, Number 1 (2012), 91-106.
The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2
For a finite group G, an L(G)-free gap G-module V is a finite dimensional real G-representation space satisfying the two conditions: (1) VL = 0 for any normal subgroup L of G with prime power index. (2) dim VP > 2 dim VH for any P < H ≤ G such that P is of prime power order. A finite group G not of prime power order is called a gap group if there is an L(G)-free gap G-module. We give a necessary and sufficient condition for that G is a gap group for a finite group G satisfying that G/[G,G] is not a 2-group, where [G,G] is the commutator subgroup of G.
J. Math. Soc. Japan, Volume 64, Number 1 (2012), 91-106.
First available in Project Euclid: 26 January 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
SUMI, Toshio. The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2. J. Math. Soc. Japan 64 (2012), no. 1, 91--106. doi:10.2969/jmsj/06410091. https://projecteuclid.org/euclid.jmsj/1327586975