The Schur multiplier of a p-group with the derived subgroup of maximal order

2020 ◽  
Vol 48 (11) ◽  
pp. 4948-4953
Author(s):  
Afsaneh Shamsaki ◽  
Peyman Niroomand ◽  
Farangis Johari
Keyword(s):  
Maximal Order ◽  
Schur Multiplier ◽  
Derived Subgroup

Some Inequalities for the Order of the Schur Multiplier of a Pair of Groups

2008 ◽  
Vol 36 (7) ◽  
pp. 2481-2486 ◽  
Author(s):  
Mohammad Reza R. Moghaddam ◽  
Ali Reza Salemkar ◽  
Taghi Karimi
Keyword(s):  
Schur Multiplier

Maximal Order of an NG-group

2021 ◽  
pp. 33-38
Author(s):  
Faraj. A. Abdunabi
Keyword(s):  
Permutation Group ◽  
Equivalence Relation ◽  
Maximal Order ◽  
Quotient Set

This study was aimed to consider the NG-group that consisting of transformations on a nonempty set A has no bijection as its element. In addition, it tried to find the maximal order of these groups. It found the order of NG-group not greater than n. Our results proved by showing that any kind of NG-group in the theorem be isomorphic to a permutation group on a quotient set of A with respect to an equivalence relation on A. Keywords: NG-group; Permutation group; Equivalence relation; -subgroup

Finite groups with two supersoluble subgroups

2019 ◽  
Vol 22 (2) ◽  
pp. 297-312 ◽  
Author(s):  
Victor S. Monakhov ◽  
Alexander A. Trofimuk
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sufficient Conditions ◽  
Maximal Subgroups ◽  
Sylow Subgroups ◽  
Derived Subgroup ◽  
Nilpotent Residual ◽  
A Finite Group

AbstractLetGbe a finite group. In this paper we obtain some sufficient conditions for the supersolubility ofGwith two supersoluble non-conjugate subgroupsHandKof prime index, not necessarily distinct. It is established that the supersoluble residual of such a group coincides with the nilpotent residual of the derived subgroup. We prove thatGis supersoluble in the following cases: one of the subgroupsHorKis nilpotent; the derived subgroup{G^{\prime}}ofGis nilpotent;{|G:H|=q>r=|G:K|}andHis normal inG. Also the supersolubility ofGwith two non-conjugate maximal subgroupsMandVis obtained in the following cases: all Sylow subgroups ofMand ofVare seminormal inG; all maximal subgroups ofMand ofVare seminormal inG.

Multiplicative Lie algebras and Schur multiplier

2019 ◽  
Vol 223 (9) ◽  
pp. 3695-3721 ◽  
Author(s):  
Ramji Lal ◽  
Sumit Kumar Upadhyay
Keyword(s):  
Lie Algebras ◽  
Schur Multiplier

On the schur multiplier ofp-groups

1999 ◽  
Vol 27 (9) ◽  
pp. 4173-4177 ◽  
Author(s):  
Graham Ellis
Keyword(s):  
Schur Multiplier

scholarly journals Automorphy factors for a Hilbert modular group

1988 ◽  
Vol 30 (2) ◽  
pp. 231-236
Author(s):  
Shigeaki Tsuyumine
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Rational Number ◽  
Modular Group ◽  
Algebraic Number Field ◽  
Maximal Order ◽  
Hilbert Modular Group ◽  
Hilbert Modular ◽  
Totally Real

Let K be a totally real algebraic number field of degree n > 1, and let OK be the maximal order. We denote by гk, the Hilbert modular group SL2(OK) associated with K. On the extent of the weight of an automorphy factor for гK, some restrictions are imposed, not as in the elliptic modular case. Maass [5] showed that the weight is integral for K = ℚ(√5). It was shown by Christian [1] that for any Hilbert modular group it is a rational number with the bounded denominator depending on the group.

scholarly journals The Maximal Order of Hyper-($b$-ary)-expansions

10.37236/5441 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Michael Coons ◽  
Lukas Spiegelhofer
Keyword(s):  
Recent Result ◽  
Nonnegative Integer ◽  
Maximal Order ◽  
General Integral ◽  
Integral Bases

Using methods developed by Coons and Tyler, we give a new proof of a recent result of Defant, by determining the maximal order of the number of hyper-($b$-ary)-expansions of a nonnegative integer $n$ for general integral bases $b\geqslant 2$.

scholarly journals Core entropy of polynomials with a critical point of maximal order

2019 ◽  
Vol 39 (1) ◽  
pp. 115-130
Author(s):  
Domingo González ◽  
◽  
Gamaliel Blé
Keyword(s):  
Critical Point ◽  
Maximal Order

scholarly journals ON THE EXPONENT OF THE SCHUR MULTIPLIER OF A PAIR OF FINITE p-GROUPS

2013 ◽  
Vol 12 (08) ◽  
pp. 1350053
Author(s):  
FAHIMEH MOHAMMADZADEH ◽  
AZAM HOKMABADI ◽  
BEHROOZ MASHAYEKHY
Keyword(s):  
Upper Bound ◽  
Schur Multiplier

In this paper, we find an upper bound for the exponent of the Schur multiplier of a pair (G, N) of finite p-groups, when N admits a complement in G. As a consequence, we show that the exponent of the Schur multiplier of a pair (G, N) divides exp (N) if (G, N) is a pair of finite p-groups of class at most p – 1. We also prove that if N is powerfully embedded in G, then the exponent of the Schur multiplier of a pair (G, N) divides exp (N).

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