## Tbilisi Mathematical Journal

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

#### Abstract

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

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

Dates
Revised: 11 May 2012
Accepted: 28 May 2012
First available in Project Euclid: 12 June 2018

https://projecteuclid.org/euclid.tbilisi/1528768887

Mathematical Reviews number (MathSciNet)
MR2950184

Zentralblatt MATH identifier
1284.20033

Keywords
$c$-capability pair of groups

#### Citation

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

#### References

• R. Baer. Groups with preassigned central and central quotient group. Trans. Amer. Math. Soc., 44 (1938), 387-412.
• F.R. Beyl, U. Felgner, P. Schmid. On groups occurring as a center factor groups. J. Algebra, 61 (1979), 161-177.
• J. Burns, G. Ellis. On the nilpotent multipliers of a group. Math. Z., 226 (1997), 405-428.
• G. Ellis. Capability, homology, and central series of a pair of groups. J. Algebra, 179 (1996), 31-46.
• M. Hall, Jr., J.K. Senior. The groups of order $2^{n}(n\leq 6)$. Macmillan Co., New York, 1964.
• P. Hall. The classification of prime power groups. J. Reine Angew. Math., 182 (1940), 130-141.
• A. Hokmabadi, F. Mohammadzadeh, S. Kayvanfar. Polynilpotent capability of some nilpotent products of cyclic groups. J. of Advanced Research in Pure Mathematics, to appear.
• A. Pourmirzaei, A. Hokmabadi, S. Kayvanfar. Capability of a pair of groups. Bulletin of the Malaysian Mathematical Sciences Society, 35 (1) (2012), 205-213.