The normal complement problem in group algebras

2021 ◽  
pp. 1-5
Author(s):  
Himanshu Setia ◽  
Manju Khan
Keyword(s):  
Group Algebras ◽  
Normal Complement

A note on normal complement problem

2017 ◽  
Vol 16 (01) ◽  
pp. 1750011 ◽  
Author(s):  
K. Kaur ◽  
M. Khan ◽  
T. Chatterjee
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Positive Characteristic ◽  
Unit Group ◽  
Semisimple Group ◽  
Group Algebras ◽  
Metacyclic Group ◽  
Infinite Class ◽  
Normal Complement ◽  
Characteristic 2

In this paper, we study the normal complement problem on semisimple group algebras and modular group algebras [Formula: see text] over a field [Formula: see text] of positive characteristic. We provide an infinite class of abelian groups [Formula: see text] and Galois fields [Formula: see text] that have normal complement in the unit group [Formula: see text] for semisimple group algebras [Formula: see text]. For metacyclic group [Formula: see text] of order [Formula: see text], where [Formula: see text] are distinct primes, we prove that [Formula: see text] does not have normal complement in [Formula: see text] for finite semisimple group algebra [Formula: see text]. Finally, we study the normal complement problem for modular group algebras over field of characteristic 2.

Golgi Apparatus and Melanogenesis: Ultrastructural Study of a Human Cellular Blue Nevus (Melanocytoma)

1973 ◽  
Vol 31 ◽  
pp. 380-381
Author(s):  
S.R. Allegra
Keyword(s):  
Endoplasmic Reticulum ◽  
Golgi Apparatus ◽  
Ultrastructural Study ◽  
The Other ◽  
Blue Nevus ◽  
Normal Complement ◽  
Golgi Vesicles ◽  
Golgi System ◽  
The Subject ◽  
Cellular Blue Nevus

The respective roles of the ribo somes, endoplasmic reticulum, Golgi apparatus and perhaps nucleus in the synthesis and maturation of melanosomes is still the subject of some controversy. While the early melanosomes (premelanosomes) have been frequently demonstrated to originate as Golgi vesicles, it is undeniable that these structures can be formed in cells in which Golgi system is not found. This report was prompted by the findings in an essentially amelanotic human cellular blue nevus (melanocytoma) of two distinct lines of melanocytes one of which was devoid of any trace of Golgi apparatus while the other had normal complement of this organelle.

Complex group algebras of the direct product of non-isomorphic Suzuki groups

2019 ◽  
Vol 19 (02) ◽  
pp. 2050036
Author(s):  
Morteza Baniasad Azad ◽  
Behrooz Khosravi
Keyword(s):  
Direct Product ◽  
Group Algebra ◽  
Irreducible Character ◽  
Prime Numbers ◽  
Product Formula ◽  
Character Degrees ◽  
Group Algebras ◽  
Complex Group ◽  
Complex Group Algebra ◽  
Suzuki Groups

In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals Dominant and global dimension of blocks of quantised Schur algebras

2021 ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Global Dimension ◽  
Group Algebras ◽  
Dominant Dimension ◽  
Schur Algebras ◽  
Homological Dimensions ◽  
Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

On *-clean non-commutative group rings

2016 ◽  
Vol 15 (08) ◽  
pp. 1650150 ◽  
Author(s):  
Hongdi Huang ◽  
Yuanlin Li ◽  
Gaohua Tang
Keyword(s):  
Finite Field ◽  
Local Ring ◽  
Group Algebra ◽  
Rational Numbers ◽  
Semisimple Group ◽  
Group Algebras ◽  
Group Rings ◽  
Dihedral Groups ◽  
Commutative Local Ring ◽  
Generalized Quaternion

A ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection (∗-invariant idempotent). In this paper, we consider the group algebras of the dihedral groups [Formula: see text], and the generalized quaternion groups [Formula: see text] with standard involution ∗. For the non-semisimple group algebra case, we characterize the ∗-cleanness of [Formula: see text] with a prime [Formula: see text], and [Formula: see text] with [Formula: see text], where [Formula: see text] is a commutative local ring. For the semisimple group algebra case, we investigate when [Formula: see text] is ∗-clean, where [Formula: see text] is the field of rational numbers [Formula: see text] or a finite field [Formula: see text] and [Formula: see text] or [Formula: see text].

OVARIAN SENSITIVITY TO OVULATORY STIMULI IN THE ANDROGEN-INDUCED PERSISTENT-OESTROUS RATS

1971 ◽  
Vol 66 (2) ◽  
pp. 266-272
Author(s):  
Anant P. Labhsetwar
Keyword(s):  
Testosterone Propionate ◽  
Ovarian Response ◽  
Minimal Amount ◽  
Normal Complement ◽  
Adult Rats ◽  
Induced Ovulation ◽  
Postnatal Treatment ◽  
Small Doses

ABSTRACT The ovarian response of adult rats made persistent-oestrus by the postnatal treatment with testosterone propionate was examined by determining the number of ova shed in response to small doses of LH and/or FSH, and placental gonadotrophins (PMSG or HCG). A dose of LH (10 μg/rat) estimated to be equivalent to twice the minimal amount secreted for ovulation in normal rats failed to release a normal complement of ova. The same dose of FSH induced ovulation in 40% of rats with an ova count of 5.7 ± 1.8/rat. Both placental gonadotrophins induced ovulation, although the ova yield was significantly below the normal oestrous control. It is inferred from these findings that the ovarian sensitivity of androgen-sterilized rats is far below that of the normal animals despite the presence of numerous follicles in the ovaries of the persistent-oestrous rats.

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