The First Sylow Theorem

2013 ◽  
pp. 469-482
Keyword(s):  
Sylow Theorem

scholarly journals More generalised Sylow theorems

1997 ◽  
Vol 62 (1) ◽  
pp. 84-92
Author(s):  
I. J. Hawthorn
Keyword(s):  
Finite Groups ◽  
Class A ◽  
Sylow Theorem ◽  
Common Framework ◽  
Fitting Classes

AbstractThe study of classes of finite groups is divided into two parts. The projective theory studies formations and Schunck classes. The dual injective theory studies Fitting classes. In each type of class a generalisation of Sylow's theorem holds. In this paper we seek further generalisations of Sylow's theorem which hold for classes which are neither injective nor projective, but obey other related properties. Firstly a common framework for the injective and projective theories is constructed. Within the context of this common framework further types of Sylow theorem can then be sought. An example is given of a property which is a simple hybrid of injectivity and projectivity which we will call ‘interjectivity’. A generalised Sylow theorem is then proved in the interjective case.

Generalizations of the Sylow theorem

2011 ◽  
pp. 488-519 ◽  
Author(s):  
Danila O. Revin ◽  
Evgeny P. Vdovin
Keyword(s):  
Sylow Theorem

scholarly journals 5G Massive Multiple Input and Multiple Output System with Maximum Spectral Performance

2020 ◽  
Vol 8 (5) ◽  
pp. 2948-2952
Keyword(s):  
Massive Mimo ◽  
Communication Systems ◽  
Additive White Gaussian Noise ◽  
Systems Design ◽  
Spatial Multiplexing ◽  
Fourth Generation ◽  
Time Frequency ◽  
Large Bandwidth ◽  
Spectral Performance ◽  
Sylow Theorem

Massive MIMO is the presently maximum compelling sub-6 GHz physical-layer era for destiny wireless access. Excellent spectral overall performance finished through manner of spatial multiplexing of many terminals inside the equal time-frequency resource. The 5G structures are characterized through excessive transmission records prices, 1Gbps and above, so large bandwidth transmission is expected. The most vital objectives within the 5G wireless systems design is to deal with the excessive inter photograph interference (ISI) as a consequence of the high statistics fees, and using the accessible spectral bandwidth in resourceful way.MC-CDMA is categorized in to two methods that is ODFM and CDMA. Efficient useful resource allocation is the principle trouble within the development of fourth generation cellular communication systems. For utilizing the internet and multimedia a maximum data fee is preferred, so in this paper the general performance of MC-CDMA systems the usage of Sylow theorem for grouping this is executed that's a spectrum allocation technique is presented. This paper particularly analyzes the presence of Additive white Gaussian Noise (AWGN) in MC-CDMA utilizing QPSK for special variety of subcarrier, exclusive wide sort of customers with the help of MATLAB tool. This paper shows the reduction in BER and power allocation among the MC-CDMA and massive-MIMO.

scholarly journals On the Existence of (v,k,λ) Difference Sets with k<1250 and k−λ Is a Square

ISRN Algebra ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Adegoke Solomon Osifodunrin
Keyword(s):  
Difference Sets ◽  
Variance Technique ◽  
Sylow Theorem

We combine Turyn's self-conjugacy result, variance technique, Dillon dihedral trick, and Sylow theorem to investigate the existence of (v,k,λ) difference sets in which k−λ is a square and k<1250.

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