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Displaying 81 – 100 of 308

Finite Groups as the Union of Proper Subgroups

Zhang, Jiping (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 20D60,20E15.As is known, if a finite solvable group G is an n-sum group then n − 1 is a prime power. It is an interesting problem in group theory to study for which numbers n with n-1 > 1 and not a prime power there exists a finite n-sum group. In this paper we mainly study finite nonsolvable n-sum groups and show that 15 is the first such number. More precisely, we prove that there exist no finite 11-sum or 13-sum groups and there is indeed a finite 15-sum...

Finite Groups Generated by 3-Transpositions. I.

B. Fischer (1971)

Inventiones mathematicae

Finite Groups have local Non-Schur Centralizers.

Peter Fleischmann, Ingo Janiszczak (1993)

Manuscripta mathematica

Finite groups in which every self-centralizing subgroup is nilpotent or subnormal or a TI-subgroup

Jiangtao Shi, Na Li (2021)

Czechoslovak Mathematical Journal

Let $G$ be a finite group. We prove that if every self-centralizing subgroup of $G$ is nilpotent or subnormal or a TI-subgroup, then every subgroup of $G$ is nilpotent or subnormal. Moreover, $G$ has either a normal Sylow $p$ -subgroup or a normal $p$ -complement for each prime divisor $p$ of $| G |$ .

Finite groups in which every two elements generate a soluble subgroup.

Paul Flavell (1995)

Inventiones mathematicae

Finite groups in which subnormalizers are subgroups

Carlo Casolo (1989)

Rendiconti del Seminario Matematico della Università di Padova

Finite groups in which Sylow normalizers have nilpotent Hall supplements.

Li, Baojun, Guo, Wenbin, Huang, Jianhong (2009)

Sibirskij Matematicheskij Zhurnal

Finite groups in which the normalizers of Sylow 3-subgroups are of odd or primary index.

Kondrat'ev, A.S., Guo, Wenbin (2009)

Sibirskij Matematicheskij Zhurnal

Finite groups in which $τ$ -quasinormality is a transitive relation

Vladimir O. Lukyanenko, Alexander N. Skiba (2010)

Rendiconti del Seminario Matematico della Università di Padova

Finite groups of automorphisms of K3 surfaces and the Mathieu group.

Shigeru Mukai (1988)

Inventiones mathematicae

Finite groups of bounded rank with an almost regular automorphism of prime order.

Khukhro, E.I. (2002)

Sibirskij Matematicheskij Zhurnal

Finite Groups of Exponent 12 as Automorphism Groups.

Kurt A. Hirsch, J. Terry Hallett (1977)

Mathematische Zeitschrift

Finite Groups of Exponent 4 as Automorphism Groups. II.

J. Terry Tallett, Hirsch Kurt A. (1973)

Mathematische Zeitschrift

Finite groups of OTP projective representation type

Leonid F. Barannyk (2012)

Colloquium Mathematicae

Let K be a field of characteristic p > 0, K* the multiplicative group of K and $G = G_{p} \times B$ a finite group, where $G_{p}$ is a p-group and B is a p’-group. Denote by $K^{λ} G$ a twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such that every indecomposable $K^{λ} G$ -module is isomorphic to the outer tensor product V W of an indecomposable $K^{λ} G_{p}$ -module V and a simple...

Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic

Leonid F. Barannyk, Dariusz Klein (2012)

Colloquium Mathematicae

Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and $G = G_{p} \times B$ a finite group, where $G_{p}$ is a p-group and B is a p’-group. Denote by $S^{λ} G$ the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such that every indecomposable...

Finite Groups of Rank 3. I.

Michael Aschbacher (1981)

Inventiones mathematicae

Finite Groups of Rank 3. II.

Michael Aschbacher (1983)

Inventiones mathematicae

Finite groups whose all proper subgroups are $𝒞$ -groups

Pengfei Guo, Jianjun Liu (2018)

Czechoslovak Mathematical Journal

A group $G$ is said to be a $𝒞$ -group if for every divisor $d$ of the order of $G$ , there exists a subgroup $H$ of $G$ of order $d$ such that $H$ is normal or abnormal in $G$ . We give a complete classification of those groups which are not $𝒞$ -groups but all of whose proper subgroups are $𝒞$ -groups.

Finite groups whose character degree graphs coincide with their prime graphs

Temha Erkoç, Utku Yilmaztürk, İsmail Ş. Güloğlu (2018)

Czechoslovak Mathematical Journal

In the literature, there are several graphs related to a finite group $G$ . Two of them are the character degree graph, denoted by $Δ (G)$ , and the prime graph, $Γ (G)$ . In this paper we classify all finite groups whose character degree graphs are disconnected and coincide with their prime graphs. As a corollary, we find all finite groups whose character degree graphs are square and coincide with their prime graphs.

Finite Groups Whose Minimal Subgroups are Normal.

Joseph Buckley (1970)

Mathematische Zeitschrift

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