On the Modular Representation Algebra Metacyclic Groups

1964 ◽  
Vol s1-39 (1) ◽  
pp. 267-276 ◽  
Author(s):  
M. F. O'Reilly
Keyword(s):  
Modular Representation ◽  
Metacyclic Groups ◽  
Representation Algebra

scholarly journals Recurrence relations in a modular representation algebra

1982 ◽  
Vol 26 (2) ◽  
pp. 215-219 ◽  
Author(s):  
J-C. Renaud
Keyword(s):  
Cyclic Group ◽  
Prime Order ◽  
Recurrence Relations ◽  
Binomial Coefficient ◽  
Modular Representation ◽  
Exterior Powers ◽  
Representation Algebra

In 1978 Almkvist and Fossum examined the decomposition of the exterior powers of basis modules in the modular representation algebra of a cyclic group of prime order. In particular they developed an isomorphism between these exterior powers and terms of binomial coefficient type in the algebra.We derive several recurrence relations for these terms.

scholarly journals The modular representation algebra of groups with Sylow 2-subgroup Z2 × Z2

1966 ◽  
Vol 6 (1) ◽  
pp. 76-88 ◽  
Author(s):  
S. B. Conlon
Keyword(s):  
Finite Group ◽  
Modular Representation ◽  
Alternating Group ◽  
Complex Numbers ◽  
Characteristic 2 ◽  
A Finite Group ◽  
Representation Algebra

Let k be a field of characteristic 2 and let G be a finite group. Let A(G) be the modular representation algebra1 over the complex numbers C, formed from kG-modules2. If the Sylow 2-subgroup of G is isomorphic to Z2×Z2, we show that A(G) is semisimple. We make use of the theorems proved by Green [4] and the results of the author concerning A(4) [2], where 4 is the alternating group on 4 symbols.

scholarly journals The characters and structure of a class of modular representation algebras of cyclic p-groups

1978 ◽  
Vol 26 (4) ◽  
pp. 410-418 ◽  
Author(s):  
J. C. Renaud
Keyword(s):  
Local Ring ◽  
Cyclic Group ◽  
Modular Representation ◽  
Alternative Proof ◽  
Local Rings ◽  
Prime Field ◽  
Direct Sum ◽  
Primitive Idempotents ◽  
C 30 ◽  
Representation Algebra

AbstractLet p,m be the modular representation algebra of the cyclic group of order pm over the prime field Zp. The characters of p, m are derived. For p = 2, this provides an alternative proof of a result due to Carlson (1975), tha 2,m is a local ring. It is shown that for p>2, p, m is a direct sum of 2m local rings. Their dimensions and primitive idempotents are derived.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 C 20, 12 C 05, 12 C 30, 33 A 65.

Relative characters for H-projective RG-lattices

1988 ◽  
Vol 104 (2) ◽  
pp. 207-213 ◽  
Author(s):  
Peter Symonds
Keyword(s):  
Representation Theory ◽  
Direct Summand ◽  
Modular Representation ◽  
Dedekind Domain ◽  
Modular Representation Theory ◽  
Trivial Group ◽  
Ordinary Character ◽  
Projective Lattices

If G is a group with a subgroup H and R is a Dedekind domain, then an H-projective RG-lattice is an RG-lattice that is a direct summand of an induced lattice for some RH-lattice N: they have been studied extensively in the context of modular representation theory. If H is the trivial group these are the projective lattices. We define a relative character χG/H on H-projective lattices, which in the case H = 1 is equivalent to the Hattori–Stallings trace for projective lattices (see [5, 8]), and in the case H = G is the ordinary character. These characters can be used to show that the R-ranks of certain H-projective lattices must be divisible by some specified number, generalizing some well-known results: cf. Corollary 3·6. If for example we take R = ℤ, then |G/H| divides the ℤ-rank of any H-projective ℤG-lattice.

scholarly journals Strong duality for metacyclic groups

2002 ◽  
Vol 73 (3) ◽  
pp. 377-392 ◽  
Author(s):  
R. Quackenbush ◽  
C. S. Szabó
Keyword(s):  
Finite Group ◽  
Dihedral Group ◽  
Strong Duality ◽  
Sylow Subgroups ◽  
Metacyclic Groups ◽  
Group D

AbstractDavey and Quackenbush proved a strong duality for each dihedral group Dm with m odd. In this paper we extend this to a strong duality for each finite group with cyclic Sylow subgroups (such groups are known to be metacyclic).

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