Tbilisi Mathematical Journal

A criterion for $c$-capability of pairs of groups

Azam Hokmabadi, Azam Pourmirzaei, and Saeed Kayvanfar

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The notion of capability for pairs of groups was defined by Ellis in 1996. In this paper, we extend the theory of $c$-capability for pairs of groups and introduce a criterion, denoted by $Z_c^*(G,N)$, for $c$-capability of a pair $(G,N)$ of groups. We also study the behavior of $Z_c^*(G,N)$ with respect to direct products of groups.

Article information

Tbilisi Math. J., Volume 5, Issue 1 (2012), 31-38.

Received: 3 May 2011
Revised: 11 May 2012
Accepted: 28 May 2012
First available in Project Euclid: 12 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F14: Derived series, central series, and generalizations
Secondary: 20F28: Automorphism groups of groups [See also 20E36]

$c$-capability pair of groups


Hokmabadi, Azam; Pourmirzaei, Azam; Kayvanfar, Saeed. A criterion for $c$-capability of pairs of groups. Tbilisi Math. J. 5 (2012), no. 1, 31--38. https://projecteuclid.org/euclid.tbilisi/1528768887

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