On the embedding of finite solvable groups

Abstract

In 1969, Seitz proved that every finite solvable group can be (isomorphically) embedded in a monomial group with the same derived length (fitting length, supersolvable length). In this paper, it is proved that every finite solvable group can in fact be embedded in a generalized strongly monomial group with the same derived length (fitting length, supersolvable length). This shows the vastness of the class of generalized strongly monomial groups.

KEYWORD:

• Generalized strongly monomial group
• monomial group
• rational group algebra
• strongly monomial group

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16S34
• 20C15
• 20C05

Acknowledgments

The author is thankful to the referee for carefully reading the manuscript and providing valuable comments and suggestions which has greatly improved the presentation of the paper.

Funding

Additional information

Funding

Research supported by Science and Engineering Research Board (SERB), DST, Govt. of India (National Post-Doctoral Fellowship Sanction Order No. PDF/2020/000343) is gratefully acknowledged.