| π Frattini Subgroup and π Local Formation |
| Received:October 07, 1996 Revised:February 16, 1998 |
| Key Words:
π-Frattini subgroup π-locally defined formation Gaschütz theorem.
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| Fund Project:Project supported by the National Natural Science Foundation of China. |
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| Abstract: |
| In this paper, our purpose is to make the results about π-Frattini subgroup more accurate, and to extend Gaschütz Theorem about nilpotency to π-locally defined formation. We come to Theorem Let G be a finite group, H a subnormal subgroup of G. If H/H∩Φ(G)O π′ (G)∈F, then H∈F π, where F π is π-solvable π-locally defined formation. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1998.02.003 |
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