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Correlation between direct product and sylows theorem on automorphic image of permutation group
International Journal of Advanced Academic Studies · 2019 · Vol. 1(1) · pp. 57–58
Amod Kumar Mishra✉(Kumar Bhaskar Varma Sanskrit and Ancient Studies University)
Abstract
We should know that the product of two sets as a set of ordered pairs. We now search a new group through the product of two groups. Let G1, G2 be any two subgroups Let G = G1G2 = [(g1, g2): g1 G1What better way could g2G2} there be than to define multiplication on G by (g1, g2) (g1'g2') = (g1 g1', g2g2'). That G forms a group under this as its composition should not be a difficult task for the reader. We focus on the matter that of G is a group of order 15; it is IDp (interval direct product) of its sylow subgroups.
graph theory and CDMA systemsFinite Group Theory ResearchCoding theory and cryptographySylow theoremsMathematicsGroup (periodic table)Direct productPermutation (music)Product (mathematics)Order (exchange)Permutation groupSet (abstract data type)Combinatorics
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