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2011•Journal of Group TheoryRequires access

The normalizer property for integral group rings of finite solvable T-groups

Zhengxing Li, Jinke Hai

Open publisher page 11 citations

Abstract

Abstract. A group is said to be a T-group if all its subnormal subgroups are normal. Let be a finite solvable T-group. It is shown that the normalizer property holds for . As a direct consequence of our result, we obtain that the normalizer property holds for finite groups all of whose Sylow subgroups are cyclic.

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What this paper is about

Abstract. A group is said to be a T-group if all its subnormal subgroups are normal. Let be a finite solvable T-group. It is shown that the normalizer property holds for . As a direct consequence of our result, we obtain that the normalizer property holds for finite groups all of whose Sylow subgroups are cyclic.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Abstract. A group is said to be a T-group if all its subnormal subgroups are normal. Let be a finite solvable T-group. It is shown that the normalizer property holds for . As a direct consequence of our result, we obtain that the normalizer property holds for finite groups all of whose Sylow subgroups are cyclic.

Key concepts: Centralizer and normalizer, Sylow theorems, Mathematics, Property (philosophy), Solvable group, Group (periodic table), Finite group, Pure mathematics

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