Open Access
June 2006 Active sums II
Alejandro J. Díaz-Barriga, Francisco González-Acuña, Francisco Marmolejo, Leopoldo Román
Osaka J. Math. 43(2): 371-399 (June 2006).

Abstract

We exhibit several finite groups that are not active sums of cyclic subgroups. We show that this is the case for groups with $H_{1}G$ of odd order and $H_{2}G$ of even order. As particular examples of this we have the alternating groups $A_n$ for $n\geq 4$, some special and some projective linear groups. Our next set of examples consists of $p$-groups where the normalizer and the centralizer of every element coincide. We also have an example of a 2-group where the above conditions are not satisfied; thus we had to devise an ad hoc argument. We observe that the examples of $p$-groups given also provide groups that are not molecular.

Citation

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Alejandro J. Díaz-Barriga. Francisco González-Acuña. Francisco Marmolejo. Leopoldo Román. "Active sums II." Osaka J. Math. 43 (2) 371 - 399, June 2006.

Information

Published: June 2006
First available in Project Euclid: 6 July 2006

zbMATH: 1121.20040
MathSciNet: MR2262341

Subjects:
Primary: 20D99 , 20J05
Secondary: 20D30

Rights: Copyright © 2006 Osaka University and Osaka City University, Departments of Mathematics

Vol.43 • No. 2 • June 2006
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