Capable groups of prime exponent and class two

2004/01/29 by Arturo Magidin, Magidin, Arturo
Computer Science · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #Rings, Modules, and Algebras #math.GR #msc:20D15 #msc:20F12

paper · pdf · doi:10.48550/arxiv.math/0401423

20 pp

arxiv created 2004/01/29 · arxiv updated 2009/12/01

Abstract

A group is called capable if it is a central factor group. We consider the capability of finite groups of class two and exponent p, p an odd prime. We restate the problem of capability as a problem about linear transformations, which may be checked explicitly for any specific instance of the problem. We use this restatement to derive some known results, and prove new ones. Among them, we reduce the general problem to an oft-considered special case, and prove that a 3-generated group of class 2 and exponent p is either cyclic or capable.

Related

• On the capability of finite groups of class two and prime exponent
• Capable groups of prime exponent and class 2, II
• Some results on capable groups of prime exponent and class two
• Capability of certain nilpotent products of cyclic groups
• On the orders of generators of capable p-groups