@Article{Kaheni2012,
author="Kaheni, Azam
and Hatamian, Rasoul
and Kayvanfar, Saeed",
title="On the groups satisfying the converse of Schur's theorem",
journal="International Journal of Group Theory",
year="2012",
volume="1",
number="4",
pages="1-7",
abstract="A famous theorem of Schur states that for a group $G$ finiteness of $G/Z(G)$ implies the finiteness of $G'.$ The converse of Schur's theorem is an interesting problem which has been considered by some authors. Recently, Podoski and Szegedy proved the truth of the converse of Schur's theorem for capable groups. They also established an explicit bound for the index of the center of such groups. This paper is devoted to determine some families of groups among non-capable groups which satisfy the converse of Schur's theorem and at the same time admit the Podoski and Szegedy's bound as the upper bound for the index of their centers.",
issn="2251-7650",
doi="10.22108/ijgt.2012.1485",
url="http://ijgt.ui.ac.ir/article_1485.html"
}
@Article{Wilkens2012,
author="Wilkens, Bettina",
title="CH-groups which are finite $p$-groups",
journal="International Journal of Group Theory",
year="2012",
volume="1",
number="4",
pages="9-23",
abstract="In their paper "Finite groups whose noncentral commuting elements have centralizers of equal size", S. Dolfi, M. Herzog and E. Jabara classify the groups in question- which they call $ CH$-groups- up to finite $p$-groups. Our goal is to investigate the finite $p$-groups in the class. The chief result is that a finite $p$-group that is a $ CH$-group either has an abelian maximal subgroup or is of class at most $p+1$. Detailed descriptions, in some cases characterisations up to isoclinism, are given.",
issn="2251-7650",
doi="10.22108/ijgt.2012.1509",
url="http://ijgt.ui.ac.ir/article_1509.html"
}
@Article{Zeng2012,
author="Zeng, Guangju",
title="Finite simple groups with number of zeros slightly greater than the number of nonlinear irreducible characters",
journal="International Journal of Group Theory",
year="2012",
volume="1",
number="4",
pages="25-32",
abstract="The aim of this paper is to classify the finite simple groups with the number of zeros at most seven greater than the number of nonlinear irreducible characters in the character tables. We find that they are exactly A$_{5}$, L$_{2}(7)$ and A$_{6}$.",
issn="2251-7650",
doi="10.22108/ijgt.2012.1518",
url="http://ijgt.ui.ac.ir/article_1518.html"
}
@Article{Sharma2012,
author="Sharma, R
and Yadav, Pooja
and Joshi, Kanchan",
title="Units in $\mathbb{Z}_2(C_2\times D_\infty)$",
journal="International Journal of Group Theory",
year="2012",
volume="1",
number="4",
pages="33-41",
abstract="In this paper we consider the group algebra $R(C_2\times D_\infty)$. It is shown that $R(C_2\times D_\infty)$ can be represented by a $4\times 4$ block circulant matrix. It is also shown that $\mathcal{U}(\mathbb{Z}_2(C_2\times D_\infty))$ is infinitely generated.",
issn="2251-7650",
doi="10.22108/ijgt.2012.1589",
url="http://ijgt.ui.ac.ir/article_1589.html"
}
@Article{Basheer2012,
author="Basheer, Ayoub Basheer Mohammed
and Moori, Jamshid",
title="Fischer matrices of Dempwolff group $2^{5}{^{\cdot}}GL(5,2)$",
journal="International Journal of Group Theory",
year="2012",
volume="1",
number="4",
pages="43-63",
abstract="In [U. Dempwolff, On extensions of elementary abelian groups of order $2^{5}$ by $GL(5,2)$, Rend. Sem. Mat. Univ. Padova, 48 (1972) 359 - 364.] Dempwolff proved the existence of a group of the form $2^{5}{^{\cdot}}GL(5,2)$ (a non split extension of the elementary abelian group $2^{5}$ by the general linear group $GL(5,2)$). This group is the second largest maximal subgroup of the sporadic Thompson simple group $\mathrm{Th}.$ In this paper we calculate the Fischer matrices of Dempwolff group $\overline{G} = 2^{5}{^{\cdot}}GL(5,2).$ The theory of projective characters is involved and we have computed the Schur multiplier together with a projective character table of an inertia factor group. The full character table of $\overline{G}$ is then can be calculated easily. ",
issn="2251-7650",
doi="10.22108/ijgt.2012.1590",
url="http://ijgt.ui.ac.ir/article_1590.html"
}
@Article{Vaughan-Lee2012,
author="Vaughan-Lee, Michael",
title="On Graham Higman's famous PORC paper",
journal="International Journal of Group Theory",
year="2012",
volume="1",
number="4",
pages="65-79",
abstract="We investigate Graham Higman's paper Enumerating $p$-groups, II, in which he formulated his famous PORC conjecture. We are able to simplify some of the theory. In particular, Higman's paper contains five pages of homological algebra which he uses in his proof that the number of solutions in a finite field to a finite set of monomial equations is PORC. It turns out that the homological algebra is just razzle dazzle, and can all be replaced by the single observation that if you write the equations as the rows of a matrix then the number of solutions is the product of the elementary divisors in the Smith normal form of the matrix. We obtain the PORC formulae for the number of $r$-generator groups of $p$ -class two for $r\leq 6$. In addition, we obtain the PORC formula for the number of $p$-class two groups of order $p^{8}$.",
issn="2251-7650",
doi="10.22108/ijgt.2012.1591",
url="http://ijgt.ui.ac.ir/article_1591.html"
}