Displaying similar documents to “On the structure of the augmentation quotient group for some nonabelian 2-groups”

A note on the transcendence of infinite products

Jaroslav Hančl, Ondřej Kolouch, Simona Pulcerová, Jan Štěpnička (2012)

Czechoslovak Mathematical Journal

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The paper deals with several criteria for the transcendence of infinite products of the form ∏ n = 1 ∞ [ b n α a n ] / b n α a n where α > 1 is a positive algebraic number having a conjugate α * such that α ≠ | α * | > 1 , { a n } n = 1 ∞ and { b n } n = 1 ∞ are two sequences of positive integers with some specific conditions. The proofs are based on the recent theorem of Corvaja and Zannier which relies on the Subspace Theorem (P. Corvaja, U. Zannier: On the rational approximation to the powers of an algebraic number: solution of two problems of Mahler and Mendès...

A note on a class of factorized p -groups

Enrico Jabara (2005)

Czechoslovak Mathematical Journal

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In this note we study finite p -groups G = A B admitting a factorization by an Abelian subgroup A and a subgroup B . As a consequence of our results we prove that if B contains an Abelian subgroup of index p n - 1 then G has derived length at most 2 n .

Unit groups of group algebras of some small groups

Gaohua Tang, Yangjiang Wei, Yuanlin Li (2014)

Czechoslovak Mathematical Journal

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Let F G be a group algebra of a group G over a field F and 𝒰 ( F G ) the unit group of F G . It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group G with order 21 over any finite field of characteristic 3 is established. We also characterize the structure of the unit group of F A 4 over any finite field of characteristic 3 and the...

Ultracompanions of subsets of a group

I. Protasov, S. Slobodianiuk (2014)

Commentationes Mathematicae Universitatis Carolinae

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Let G be a group, β G be the Stone-Čech compactification of G endowed with the structure of a right topological semigroup and G * = β G ∖ G . Given any subset A of G and p ∈ G * , we define the p -companion Δ p ( A ) = A * ∩ G p of A , and characterize the subsets with finite and discrete ultracompanions.