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The Relationship between Arithmetics and Infinite Series of Indecomposable Integral Representations of Finite Groupsopenaire +1 more source
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On Integral Absolutely Irreducible Representations of Finite Groups
Journal of Algebra and Its Applications, 2016We consider the arithmetic background of integral representations of finite groups over [Formula: see text]-adic and algebraic number rings. Some infinite series of integral pairwise inequivalent absolutely irreducible representations of finite [Formula: see text]-groups with the extra congruence conditions are constructed, and some applications are ...
Dmitry Malinin
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Globally Irreducible Representations of Finite Groups and Integral Lattices
Geometriae Dedicata, 1997Let \(G\) be a finite group, \(V\) a finite dimensional \(\mathbb{Q} G\)-module and \(\mathbb{K}=\text{End}_G(V)\). Let \(R\) be a maximal order in \(\mathbb{K}\) and \(\Lambda\) be an \(RG\)-lattice in \(V\). If \(\wp\) is a maximal two-sided ideal of \(R\), then consider the reduced representation \(V_\wp=\Lambda/\wp\Lambda\) of \(G\) over \(k_\wp=R/\
Pham Huu Tiep
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ON MODULAR AND INTEGRAL REPRESENTATION ALGEBRAS ON FINITE GROUPS
Mathematics of the USSR-Izvestiya, 1973This paper contains a solution to the semisimplicity problem for modular and integral representation algebras of finite groups over an arbitrary field. (Some of the results of this paper were announced in Dokl. Akad. Nauk SSSR 198 (1971), 509-512 = Soviet Math. Dokl. 12 (1971), 817-821; MR 43 #7522.)
Gudivok, P. M., Rud'ko, V. P.
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FINITE-DIMENSIONAL ALGEBRAS OF INTEGRAL $ p$-ADIC REPRESENTATIONS OF FINITE GROUPS
Mathematics of the USSR-Sbornik, 1974Let be a finite extension of the field of rational -adic numbers , the ring of integers of , a finite group, the ring of -representations of and ( is the ring of rational integers and the rational number field). We study the algebra in the case where the number of indecomposable -representations of is finite.
Gudivok, P. M. +2 more
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Chernikov p-groups and integral p-adic representations of finite groups
Ukrainian Mathematical Journal, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gudivok, P. M. +2 more
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On -Adic Integral Representations of Finite Groups
Canadian Journal of Mathematics, 1953It has been shown by Diederichsen [2] that for integral representations of a finite group, the irreducible constituents in any complete reduction are not necessarily unique up to order and unimodular equivalence.
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Tensor products of irreducible integral p-adic representations of finite groups
Ukrainian Mathematical Journal, 1983Let \(G\) be a finite group of order \(| G|\), \(K\) a field. Denote by \(a(KG)\) the commutative ring generated by all \(K\)-free finitely generated \(KG\)-modules, \(A_q(KG) = F_q\otimes_{{\mathbb{Z}}}a(KG)\) where \(F_q\) is a field of characteristic \(q\geq 0\). Obviously \(A_q(KG)\) has a basis of indecomposable \(KG\)-modules.
Gudivok, P. M. +2 more
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Free-by-finite pro-p groups and integral p-adic representations
Archiv der Mathematik, 2011The paper under review is a contribution to the theory of integral \(p\)-adic representations of finite \(p\)-groups. Given a free pro-\(p\) group \(F_n\) of finite rank \(n\), the natural epimorphism of \(F_n\) onto its quotient over the closure of its derived subgroup induces an epimorphism of the group \(\Aut(F_n)\) of automorphisms of \(F_n\) onto \
Porto, Anderson L. P. +1 more
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