Volume : VI, Issue : I, January - 2017

ABELIAN PROPERTIES OF SOLVABLE GROUPS AND ITS IRREDUCIBLE CHARACTER

Dr. Pankaj Kumar Chaudhary, Dr. Jawahar Lal Chaudhary

Abstract :

 Our main aim to obtain whether there exists any groups where e4 −e3 < |G| < e4 +e3. Also, there is no concrete proof that the such group cannot exist. From assumptions of theorem, it is know that if such a group does exist, then all the normal subgroups of G must be nonabelian. we examine whether the bound |G| ≤ e4 − e3 can be proved when G is a simple group. Durfee and Jensen proved that if G has a nontrivial, abelian normal sub- group, then G has a normal subgroup N so that (G,N) is a p-Gagola pair for some prime p. Thus, if there exists a group G with e4 − e3 > |G|, then d > e2 − e and all the nontrivial, normal subgroups of G are nonabelian.

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Article: Download PDF    DOI : https://www.doi.org/10.36106/gjra  

Cite This Article:

Dr. Pankaj Kumar Chaudhary, Dr. Jawahar Lal Chaudhary, ABELIAN PROPERTIES OF SOLVABLE GROUPS AND ITS IRREDUCIBLE CHARACTER, GLOBAL JOURNAL FOR RESEARCH ANALYSIS : Volume-6, Issue-1, January‾2017


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