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Degree homogeneous subgroups
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2004 |
| Abstract | Let G be a finite group and H be a subgroup. We say that H is degree homogeneous if, for each χ ∈ Irr(G), all the irreducible constituents of the restriction χH have the same degree. Subgroups which are either normal or abelian are obvious examples of degree homogeneous subgroups. Following a question by E. M. Zhmud’, we investigate general properties of such subgroups. It appears unlikely that degree homogeneous subgroups can be characterized entirely by abstract group properties, but we provide mixed criteria (involving both group structure and character properties) which are both necessary and sufficient. For example, H is degree homogeneous in G if and only if the derived subgroup H ′ is normal in G and, for every pair α, β of irreducible G-conjugate characters of H , all irreducible constituents of αH and βH have the same degree. Received by the editors March 12, 2003. The first author acknowledges partial support from NSERC Operating Grant A7171. The second author’s visit to Carleton University was made possible through this grant and he also thanks Carleton University for its hospitality during the time that this paper was written. AMS subject classification: 20C15. c ©Canadian Mathematical Society 2005. 41 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://math.carleton.ca/~jdixon/DegHomo.pdf |
| Alternate Webpage(s) | http://people.math.carleton.ca/~jdixon/DegHomo.pdf |
| Alternate Webpage(s) | https://cms.math.ca/cmb/abstract/pdf/149696.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Degree (graph theory) Edmund M. Clarke Immunostimulating conjugate (antigen) Insulin Receptor-Related Receptor, human Irreducibility Mathematics Subject Classification Personality Character Subgroup A Nepoviruses |
| Content Type | Text |
| Resource Type | Article |
