



1
Title: On Recognition by Order and Degree Pattern of Finite Simple Groups
Vol.39(2) (2015) page: 163172
Author(s): B. Akbari and A.R. Moghaddamfar
Abstract: Let GK(G) be the prime graph associated with a finite group G and D(G) be the degree pattern of G. A finite group G is said to be kfold ODcharacterizable if there exist exactly k nonisomorphic groups H such that H=G and D(H)=D(G). A 1fold ODcharacterizable group is simply called ODcharacterizable. The purpose of this paper is twofold. First, it lists a number of such simple groups that have been already investigated. Second, it shows that the simple groups L_{6}(3) and U_{4}(5) are ODcharacterizable, too.
Keywords: Prime graph; Degree pattern; Simple group. 
2
Title: Some Properties of AutoCoset Groups
Vol.39(2) (2015) page: 173179
Author(s): M. Badrkhani Asl, M.R.R. Moghaddam and M.J. Sadeghifard
Abstract: We call G to be an autocoset group, if it contains a proper characteristic subgroup N such that xN={α(x)  α ∈ Aut(G)}, for all x ∈ G\N. Clearly, if N is a normal subgroup and α runs over the inner automorphisms of G, one obtains the notion of concos groups, which was first introduced by Muktibodh in 2006. In the present article we discuss some properties of the new notion. We also introduce the concept of nautocoset and nautoCamina groups and give their connections to the groups with the property P, where P is the class of all finite groups such that their absolute centre is the same as autocommutator subgroup of order p.
Keywords: Concos group; Autoextraspecial pgroup; AutoCamina group. 
3
Title: Quasirecognition by Prime Graph of the Simple Group Bn(2)
Vol.39(2) (2015) page: 181193
Author(s): S.S. Beynekalaei, A. Iranmanesh and M.F. Ghasemabadi
Abstract: Let G be a finite group. The prime graph GK(G) of G is defined as follows. The vertices of GK(G) are the primes dividing the order of G and two distinct vertices p, q are joined by an edge if G has an element of order pq. In this paper as the main result, we show that if G is a finite group such that GK(G)=GK(B_{n}(2)), where n ≥ 8 is even, then G has a unique nonabelian composition factor isomorphic to B_{n}(2).
Keywords: Finite simple groups and their classification; Prime graph; Quasirecognition. 
4
Title: Groups in Which Every Normal Subgroup of Infinite Rank Has Finite Index
Vol.39(2) (2015) page: 195201
Author(s): M. De Falco, F. De Giovanni and C. Musella
Abstract: An infinite group is called justinfinite if all its nontrivial normal subgroups have finite index. It is proved here that if all normal subgroups of infinite rank of a radical group G have finite index, then G has finite rank.
Keywords: Justinfinite; Finite index; Finite rank; Infinite rank. 
5
Title: Some New Ideas and Results on Partially Soluble Finite Groups
Vol.39(2) (2015) page: 203218
Author(s): W. Guo, K.P. Shum and A.N. Skiba
Abstract: In this paper, some new ideas, recent results and some open questions in the theory of finite partially soluble groups will be given and discussed.
Keywords: Finite groups; Fhypercentre; Soluble groups; Supersoluble groups; Nilpotent groups; Quasisoluble groups; Quasisupersoluble groups; Quasinilpotent groups; Saturated formations; Baerlocal formations; The generalized Fitting subgroups. 
6
Title: On Autonipoltent Groups
Vol.39(2) (2015) page: 219224
Author(s): S. Hoseini, M.R.R. Moghaddam and S. Tajnia
Abstract: The concept of autonilpotent groups was introduced by Parvaneh and Mogha
ddam in 2010. In the present article, we give some classification of such groups. In final section, we introduce selfautopermutable subgroups for finite groups and obtain some more properties of autonilpotent groups.
Keywords: Autonilpotent group; Permutable subgroup; Autopermutable subgroup; Selfautopermutable subgroup. 
7
Title: On Q??Supplemented Subgroups of Finite Groups
Vol.39(2) (2015) page: 225233
Author(s): A. Mahboob, L. Zhang and Y.F. Liu
Abstract: A subgroup H of G is called QΦsupplemented in G if there exists a subgroup T of G such that G=HT and (H ∩T)H_{G}/H_{G} ≤ Φ(H/H_{G}), where H_{G} is the maximal normal subgroup of G contained in H and Φ(H/H_{G}) is the Frattini subgroup of H/H_{G}. In this paper, we study the properties of the QΦsupplemented subgroups and use them to determine the structure of finite groups.
Keywords: Sylow psubgroup; Q??supplemented subgroup; pnilpotent group; Supersoluble group. 
8
Title: A Quantitative Characterization of Mathieu Group M12
Vol.39(2) (2015) page: 235248
Author(s): A.R. Moghaddamfar and S. Rahbariyan
Abstract: Given a group G, we denote by π_{e}(G) the set of orders of elements in G. For a natural number m, we denote by s_{m}(G) the number of elements of order m in G, and put nse(G)={s_{m}(G)  m ∈ π_{e}(G)}. The group M is said to be characterizable by NSE if, for every group G, the equality nse(G)=nse(M) implies that G ≅ M. In the present article, we prove that the Mathieu group M_{12} is characterizable by NSE. This finishes the proof of the characterizability by NSE of all Mathieu simple groups. Thus, some recent results given by C.G. Shao and Q.H. Jiang in 2014 are strengthened in this paper.
Keywords: Mathieu group M12; Element order. 
9
Title: On a Maximal Subgroup of O+10 (2)
Vol.39(2) (2015) page: 249263
Author(s): J. Moori and T.T. Seretlo
Abstract: The group ?DG = 2^{8}:O_{8}^{+}(2) has order 44590694400 and is a maximal subgroup of index 527 of O_{10}^{+}(2). However 2^{10 + 16}^{.}O_{10}^{+}(2) is a maximal subgroup of the monster M = F_{1}. The group ?DG has three inertia factor groups namely, O_{8}^{+}(2), SP(6,2) and 2^{6}:A_{8} of indices 1, 120 and 135 respectively in O_{8}^{+}(2). The aim of this paper is to compute the FischerClifford matrices of ?DG, which together with associated partial character tables of the inertia factor groups, are used to compute the full character table of ?DG. There are 53 FischerClifford matrices with sizes between 1 ×1 and 6 ×6. We also compute the abstract specification of ?DG.
Keywords: Group extensions; Orthogonal groups; Character table; Clifford theory; Inertia groups; FischerClifford matrices. 
10
Title: On AutoEngle Groups and AutoBell Groups
Vol.39(2) (2015) page: 265272
Author(s): M.A. Rostamyari, A.K. Mousavi and M.R.R. Moghaddam
Abstract: The third author et al. in 2013, introduced and studied the concept of autoBell groups. A group G is said to be nautoBell if [x^{n},α]=[x,α^{n}], for all x in G, α in Aut(G) and any integer n\noindentt = 0,1. Let L_{n}(G) be the n^{th}absolute centre of the group G, then some sharp bounds for the exponents of G/L_{2}(G) and G/L_{3}(G) are constructed, when G is an nautoBell abelian or nautoBell groups. Finally, we show that ⟨ϕ_{x},α⟩ is nilpotent of class at most 4, for every inner automorphism ϕ_{x} induced by an element x of G and α in Aut(G), when G is a 3autoEngel group.
Keywords: AutoBell group; AutoEngel group; AutoKappe group; Autocommutator subgroup. 
11
Title: Some New Results on Autoisoclinism of Groups
Vol.39(2) (2015) page: 273279
Author(s): M.J. Sadeghifard, M. Eshrati and M.R.R. Moghaddam
Abstract: P. Hall in 1940 introduced the concept of isoclinism between two groups, which is weaker than isomorphism. In this article, the concept of autoisoclinism will be introduced and studied some of its properties. Among other results, we show that the properties of autonilpotency and autosolubility are invariant under this new notion.
Keywords: Isoclinism; Autoisoclinism; Autonilpotent; Autosoluble groups. 
12
Title: On the Classification of 2Step Nilpotent Zinbiel 3Algebras
Vol.39(2) (2015) page: 279290
Author(s): F. Saeedi and S.N. Akbarossadat
Abstract: In this paper, we introduce the concept of Zinbiel nalgebra and study some of its properties. Also, we explain the relation between Leibniz nalgebras and Zinbiel nalgebras. Finally, we classify some nilpotent Zinbiel nalgebras.
Keywords: Leibniz nalgebra; Zinbiel nalgebra; Nilpotent Zinbiel algebra. 
12 Records!





