A generalized Frattini subgroup of a finite group
For a finite group G and an arbitrary prime p, let SP(G) denote the intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set SP(G) = G. Some properties of G are considered involving SP(G). In particular, we obtain a characteriz...
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| Format: | Article |
| Language: | English |
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Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117128900030X |
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| _version_ | 1849408208122150912 |
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| author | Prabir Bhattacharya N. P. Mukherjee |
| author_facet | Prabir Bhattacharya N. P. Mukherjee |
| author_sort | Prabir Bhattacharya |
| collection | DOAJ |
| description | For a finite group G and an arbitrary prime p, let SP(G) denote the intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set SP(G) = G. Some properties of G are considered involving SP(G). In particular, we obtain a characterization of G when each M in the definition of SP(G) is nilpotent. |
| format | Article |
| id | doaj-art-3a54fd6bcbce40b8903f5eb366390e67 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3a54fd6bcbce40b8903f5eb366390e672025-08-20T03:35:51ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-0112226326610.1155/S016117128900030XA generalized Frattini subgroup of a finite groupPrabir Bhattacharya0N. P. Mukherjee1Department of Computer Science, University of Nebraska - Lincoln, Lincoln 68588-0115, NE, USASchool of Computer and System Sciences, Jawaharlal Nehru University, New Delhi 110067, IndiaFor a finite group G and an arbitrary prime p, let SP(G) denote the intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set SP(G) = G. Some properties of G are considered involving SP(G). In particular, we obtain a characterization of G when each M in the definition of SP(G) is nilpotent.http://dx.doi.org/10.1155/S016117128900030X |
| spellingShingle | Prabir Bhattacharya N. P. Mukherjee A generalized Frattini subgroup of a finite group International Journal of Mathematics and Mathematical Sciences |
| title | A generalized Frattini subgroup of a finite group |
| title_full | A generalized Frattini subgroup of a finite group |
| title_fullStr | A generalized Frattini subgroup of a finite group |
| title_full_unstemmed | A generalized Frattini subgroup of a finite group |
| title_short | A generalized Frattini subgroup of a finite group |
| title_sort | generalized frattini subgroup of a finite group |
| url | http://dx.doi.org/10.1155/S016117128900030X |
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