Vertices for characters of solvable groups
Author:
Gabriel Navarro
Journal:
Trans. Amer. Math. Soc. 354 (2002), 27592773
MSC (2000):
Primary 20C15
Published electronically:
March 14, 2002
MathSciNet review:
1895202
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Suppose that is a finite solvable group. We associate to every irreducible complex character of a canonical pair , where is a subgroup of and , uniquely determined by up to conjugacy. This pair behaves as a Green vertex and partitions into ``families" of characters. Using the pair , we give a canonical choice of a certain radical subgroup of and a character associated to which was predicted by some conjecture of G. R. Robinson.
 [1]
Laurence
Barker, Defects of irreducible characters of 𝑝soluble
groups, J. Algebra 202 (1998), no. 1,
178–184. MR 1614190
(99b:20014), http://dx.doi.org/10.1006/jabr.1997.7139
 [2]
Dilip
Gajendragadkar, A characteristic class of characters of finite
𝜋separable groups, J. Algebra 59 (1979),
no. 2, 237–259. MR 543247
(82b:20012), http://dx.doi.org/10.1016/00218693(79)901248
 [3]
I.
M. Isaacs, Characters of 𝜋separable groups, J.
Algebra 86 (1984), no. 1, 98–128. MR 727371
(85h:20012), http://dx.doi.org/10.1016/00218693(84)900589
 [4]
I.
Martin Isaacs, Character theory of finite groups, Academic
Press [Harcourt Brace Jovanovich Publishers], New York, 1976. Pure and
Applied Mathematics, No. 69. MR 0460423
(57 #417)
 [5]
I.
M. Isaacs and Gabriel
Navarro, Weights and vertices for characters of 𝜋separable
groups, J. Algebra 177 (1995), no. 2,
339–366. MR 1355204
(97a:20006), http://dx.doi.org/10.1006/jabr.1995.1301
 [6]
I. M. Isaacs, G. Navarro, Characters of degree of solvable groups, to appear in J. Algebra.
 [7]
Reinhard
Knörr, On the vertices of irreducible modules, Ann. of
Math. (2) 110 (1979), no. 3, 487–499. MR 554380
(81f:20013), http://dx.doi.org/10.2307/1971234
 [8]
G.
Navarro, Characters and blocks of finite groups, London
Mathematical Society Lecture Note Series, vol. 250, Cambridge
University Press, Cambridge, 1998. MR 1632299
(2000a:20018)
 [9]
G. Navarro, Induction of characters and subgroups, to appear in J. Algebra.
 [10]
Geoffrey
R. Robinson, Local structure, vertices and Alperin’s
conjecture, Proc. London Math. Soc. (3) 72 (1996),
no. 2, 312–330. MR 1367081
(97c:20015), http://dx.doi.org/10.1112/plms/s372.2.312
 [11]
Geoffrey
R. Robinson, Dade’s projective conjecture for
𝑝solvable groups, J. Algebra 229 (2000),
no. 1, 234–248. MR 1765780
(2001h:20013), http://dx.doi.org/10.1006/jabr.2000.8307
 [12]
Thomas
R. Wolf, Variations on McKay’s character degree
conjecture, J. Algebra 135 (1990), no. 1,
123–138. MR 1076081
(91h:20023), http://dx.doi.org/10.1016/00218693(90)90153F
 [1]
 L. Barker, Defects of irreducible characters of soluble groups, J. Algebra 202 (1998), 178184. MR 99b:20014
 [2]
 D. Gajendragadkar, A characteristic class of characters of finite separable groups, J. Algebra 59 (1979), 237259. MR 82b:20012
 [3]
 I. M. Isaacs, Characters of separable groups, J. Algebra 86 (1984), 98128. MR 85h:20012
 [4]
 I. M. Isaacs, Character Theory of Finite Groups, Dover, New York, 1994. MR 57:417 (1st ed.)
 [5]
 I. M. Isaacs, G. Navarro, Weights and vertices for characters of separable groups, J. Algebra 177 (1995), 339366. MR 97a:20006
 [6]
 I. M. Isaacs, G. Navarro, Characters of degree of solvable groups, to appear in J. Algebra.
 [7]
 R. Knörr, On the vertices of irreducible modules, Annals of Mathematics 110 (1979), 487499. MR 81f:20013
 [8]
 G. Navarro, Characters and Blocks of Finite Groups, London Math. Soc. Lecture Note Series 250, Cambridge University Press, 1998. MR 2000a:20018
 [9]
 G. Navarro, Induction of characters and subgroups, to appear in J. Algebra.
 [10]
 G. R. Robinson, Local structure, vertices and Alperin's conjecture, Proc. London Math. Soc. (3) 72, (1996), 312330. MR 97c:20015
 [11]
 G. R. Robinson, Dade's projective conjecture for solvable groups. J. Algebra 229 (2000), 234248. MR 2001h:20013
 [12]
 T. R. Wolf, Variations on McKay's character degree conjecture, J. Algebra 135 (1990), 123138. MR 91h:20023
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC (2000):
20C15
Retrieve articles in all journals
with MSC (2000):
20C15
Additional Information
Gabriel Navarro
Affiliation:
Departament d’Àlgebra, Facultat de Matemàtiques, Universitat de València, 46100 Burjassot. València, Spain
Email:
gabriel@uv.es
DOI:
http://dx.doi.org/10.1090/S0002994702029744
PII:
S 00029947(02)029744
Received by editor(s):
March 10, 2001
Received by editor(s) in revised form:
October 10, 2001
Published electronically:
March 14, 2002
Additional Notes:
Research partially supported by DGICYT and MEC
Article copyright:
© Copyright 2002 American Mathematical Society
