Subgroups of groups of central type
Author:
Kathleen M. Timmer
Journal:
Trans. Amer. Math. Soc. 189 (1974), 133161
MSC:
Primary 20C15
MathSciNet review:
0357574
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Let be a linear character on the center Z of a finite group Z of a finite group H, such that (1) where the 's are inequivalent irreducible characters on H of the same degree, and (2) if for some and nonnegative integers , then either for all i or for all i, j. The object of the paper is to describe finite groups which satisfy conditions (1) and (2) in terms of the multiplication of the group. If S is a p Sylow subgroup of the group H, and , then H satisfies conditions (1) and (2) if and only if (a) consists of elements of order a power of p in , and these elements form p conjugacy classes of , and (b) the elements of form p conjugacy classes of .
 [1]
F.
R. DeMeyer, Galois theory in separable algebras over commutative
rings, Illinois J. Math. 10 (1966), 287–295. MR 0191922
(33 #149)
 [2]
Frank
DeMeyer, Groups with an irreducible character
of large degree are solvable, Proc. Amer. Math.
Soc. 25 (1970),
615–617. MR 0274605
(43 #368), http://dx.doi.org/10.1090/S00029939197002746056
 [3]
Frank
R. DeMeyer and Gerald
J. Janusz, Finite groups with an irreducible representation of
large degree, Math. Z. 108 (1969), 145–153. MR 0237629
(38 #5910)
 [4]
Charles
W. Curtis and Irving
Reiner, Representation theory of finite groups and associative
algebras, Pure and Applied Mathematics, Vol. XI, Interscience
Publishers, a division of John Wiley & Sons, New YorkLondon, 1962. MR 0144979
(26 #2519)
 [5]
B.
Huppert, Endliche Gruppen. I, Die Grundlehren der
Mathematischen Wissenschaften, Band 134, SpringerVerlag, BerlinNew York,
1967 (German). MR 0224703
(37 #302)
 [6]
Herbert
Pahlings, Gruppen mit irreduziblen Darstellungen hohen Grades,
Mitt. Math. Sem. Giessen Heft 85 (1970), 27–44
(German). MR
0263938 (41 #8537)
 [1]
 F. R. DeMeyer, Galois theory in separable algebras over commutative rings, Illinois J. Math. 10 (1966), 287295. MR 0191922 (33:149)
 [2]
 , Groups with an irreducible character of large degree are solvable, Proc. Amer. Math. Soc. 25 (1970), 615617. MR 0274605 (43:368)
 [3]
 F. R. DeMeyer and G. J. Janusz, Finite groups with an irreducible representation of large degree, Math. Z. 108 (1969), 145153. MR 0237629 (38:5910)
 [4]
 C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Pure and Appl. Math., vol. 11, Interscience, New York, 1962. MR 26 #2519. MR 0144979 (26:2519)
 [5]
 B. Huppert, Endliche Gruppen I, Die Grundlehren der math. Wissenschaften, Band 134, SpringerVerlag, Berlin, 1967. MR 37 #302. MR 0224703 (37:302)
 [6]
 Herbert Pahling, Gruppen mit irreduziblen Darstellungen hohen Grades, Mitt. Math. Sem. Giessen 85 (1970), 2744. MR 41 #8537. MR 0263938 (41:8537)
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC:
20C15
Retrieve articles in all journals
with MSC:
20C15
Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197403575748
PII:
S 00029947(1974)03575748
Keywords:
Character,
representation,
group of central type,
character of large degree,
projective representation,
projective group algebra
Article copyright:
© Copyright 1974
American Mathematical Society
