한국수학사학회지 (Journal for History of Mathematics)

한국수학사학회 (The Korean Society for History of Mathematics)
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A note on M-groups

  • 발행 : 1999.12.01
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초록

Every finite solvable group is only a subgroup of an M-groups and all M-groups are solvable. Supersolvable group is an M-groups and also subgroups of solvable or supersolvable groups are solvable or supersolvable. But a subgroup of an M-groups need not be an M-groups . It has been studied that whether a normal subgroup or Hall subgroup of an M-groups is an M-groups or not. In this note, we investigate some historical research background on the M-groups and also we give some conditions that a normal subgroup of an M-groups is an M-groups and show that a solvable group is an M-group.

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참고문헌

  1. Trudy Sem. Petrovsk v.4 On normal subgroups of M-groups I. Chubarov
  2. Methods of representation C. Curtis;I. Reiner
  3. Math. Z. v.133 Normal subgroups of M-groups need not be M-groups E.C. Dade
  4. Endliche Gruppen v.I B. Juppert
  5. Character theory of finite groups M. Isaacs
  6. Arch. Math. v.42 Characters of subnormal subgroups of M-groups M. Isaacs
  7. Math. Z. v.177 Primitive characters, Normal subgroups, and M-groups M. Isaacs
  8. Proc. AMS. v.109 Hall subgroup normalizers and characters Correspondences in M-groups M. Isaacs
  9. Algebra, a graduate course M. Isaacs
  10. J. Algebra v.183 Characters of maximal subgroups of M-groups M. Lewis
  11. Proc. AMS v.125 Primitive characters of subgroups of M-groups M. Lewis
  12. Math. Z. v.218 Primitive characters of subgroups of M-groups G. Navarro
  13. Group theory E. Schenkman
  14. Hokkaido Math. J. v.10 Module correspondence in finite groups T. Okuyama
  15. Group theory II M. Suzuki
  16. Proc. Jap. Imp. Acad. v.6 Uber die gruppen, dem dar stellungen sich samtlich auf monomiale gestalt transformieren lassen K. Taketa