The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish
Pages (from-to)91-106
Number of pages16
JournalJournal of the Mathematical Society of Japan
Volume64
Issue number1
DOIs
Publication statusPublished - Oct 5 2012

Fingerprint

Quotient group
Abelian group
Finite Group
Power Indices
Commutator subgroup
Module
Normal subgroup
Necessary Conditions
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{22b1bf78f32245d3ab9aabd4c8ccf337,
title = "The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2",
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.",
author = "Toshio Sumi",
year = "2012",
month = "10",
day = "5",
doi = "10.2969/jmsj/06410091",
language = "English",
volume = "64",
pages = "91--106",
journal = "Journal of the Mathematical Society of Japan",
issn = "0025-5645",
publisher = "The Mathematical Society of Japan",
number = "1",

}

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.

UR - http://www.scopus.com/inward/record.url?scp=84866942403&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866942403&partnerID=8YFLogxK

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 -