scholarly journals Groups of central units of rank 1 of integral group rings of Frobenius metacyclic groups

2021 ◽  
Vol 18 (1) ◽  
pp. 622-639
Author(s):  
E. O. Shumakova
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Metacyclic Groups ◽  
Integral Group Rings

scholarly journals Torsion units in integral group rings of metacyclic groups

1984 ◽  
Vol 19 (1) ◽  
pp. 103-114 ◽  
Author(s):  
César Polcino Milies ◽  
Sudarshan K. Sehgal
Keyword(s):  
Group Rings ◽  
Integral Group ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Torsion Units

Units of Integral Group Rings of Some Metacyclic Groups

1994 ◽  
Vol 37 (2) ◽  
pp. 228-237 ◽  
Author(s):  
Eric Jespers ◽  
Guilherme Leal ◽  
C. Polcino Milies
Keyword(s):  
Finite Index ◽  
Unit Group ◽  
Group Algebras ◽  
Group Rings ◽  
Integral Group ◽  
Rational Group ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Almost All ◽  
Natural Way

AbstractIn this paper, we consider all metacyclic groups of the type 〈a,b | an - 1, b2 = 1, ba = aib〉 and give a concrete description of their rational group algebras. As a consequence we obtain, in a natural way, units which generate a subgroup of finite index in the full unit group, for almost all such groups.

scholarly journals TORSION UNITS IN INTEGRAL GROUP RINGS OF CERTAIN METABELIAN GROUPS

2008 ◽  
Vol 51 (2) ◽  
pp. 363-385 ◽  
Author(s):  
Martin Hertweck
Keyword(s):  
Finite Group ◽  
Abelian Group ◽  
Group Rings ◽  
Integral Group ◽  
Metabelian Groups ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Torsion Unit ◽  
A Finite Group ◽  
Torsion Units

AbstractIt is shown that any torsion unit of the integral group ring $\mathbb{Z}G$ of a finite group $G$ is rationally conjugate to an element of $\pm G$ if $G=XA$ with $A$ a cyclic normal subgroup of $G$ and $X$ an abelian group (thus confirming a conjecture of Zassenhaus for this particular class of groups, which comprises the class of metacyclic groups).

scholarly journals Picard groups and automorphism groups of integral group rings of metacyclic groups

1982 ◽  
Vol 77 (2) ◽  
pp. 286-310 ◽  
Author(s):  
Shizuo Endo ◽  
Takehiko Miyata ◽  
Katsusuke Sekiguchi
Keyword(s):  
Automorphism Groups ◽  
Group Rings ◽  
Integral Group ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Picard Groups

Units in Integral Group Rings of Some Metacyclic Groups

1987 ◽  
Vol 30 (2) ◽  
pp. 231-240 ◽  
Author(s):  
P. J. Allen ◽  
C. Hobby
Keyword(s):  
Group Ring ◽  
Multiplicative Group ◽  
Group Rings ◽  
Integral Group ◽  
Normal Complement ◽  
Metacyclic Groups ◽  
Integral Group Rings ◽  
Explicit Characterization ◽  
Normalized Units

AbstractLet p be odd prime and suppose that G = 〈a, b〉 where ap-1 = bp = 1, a-1 ba = br, and r is a generator of the multiplicative group of integers mod p. An explicit characterization of the group of normalized units V of the group ring ZG is given in terms of a subgroup of GL(p - 1, Z). This characterization is used to exhibit a normal complement for G in V.

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