Abstract
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) V L = 0 for any normal subgroup L of G with prime power index. (2) dim V P > 2 dim V H 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.
| Original language | English |
|---|---|
| Pages (from-to) | 91-106 |
| Number of pages | 16 |
| Journal | Journal of the Mathematical Society of Japan |
| Volume | 64 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Oct 5 2012 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2. / Sumi, Toshio.
In: Journal of the Mathematical Society of Japan, Vol. 64, No. 1, 05.10.2012, p. 91-106.Research output: Contribution to journal › Article
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TY - JOUR
T1 - The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2
AU - Sumi, Toshio
PY - 2012/10/5
Y1 - 2012/10/5
N2 - 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) V L = 0 for any normal subgroup L of G with prime power index. (2) dim V P > 2 dim V H 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.
AB - 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) V L = 0 for any normal subgroup L of G with prime power index. (2) dim V P > 2 dim V H 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.
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U2 - 10.2969/jmsj/06410091
DO - 10.2969/jmsj/06410091
M3 - Article
VL - 64
SP - 91
EP - 106
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
SN - 0025-5645
IS - 1
ER -