Metamath Proof Explorer


Table of Contents - 18.1. Additional material on group theory (deprecated)

This section contains an earlier development of groups that was defined before extensible structures were introduced.

The intent is for this deprecated section to be deleted once the corresponding definitions and theorems for complex topological vector spaces, which are using them, are revised accordingly.

  1. Definitions and basic properties for groups
    1. cgr
    2. cgi
    3. cgn
    4. cgs
    5. df-grpo
    6. df-gid
    7. df-ginv
    8. df-gdiv
    9. isgrpo
    10. isgrpoi
    11. grpofo
    12. grpocl
    13. grpolidinv
    14. grpon0
    15. grpoass
    16. grpoidinvlem1
    17. grpoidinvlem2
    18. grpoidinvlem3
    19. grpoidinvlem4
    20. grpoidinv
    21. grpoideu
    22. grporndm
    23. 0ngrp
    24. gidval
    25. grpoidval
    26. grpoidcl
    27. grpoidinv2
    28. grpolid
    29. grporid
    30. grporcan
    31. grpoinveu
    32. grpoid
    33. grporn
    34. grpoinvfval
    35. grpoinvval
    36. grpoinvcl
    37. grpoinv
    38. grpolinv
    39. grporinv
    40. grpoinvid1
    41. grpoinvid2
    42. grpolcan
    43. grpo2inv
    44. grpoinvf
    45. grpoinvop
    46. grpodivfval
    47. grpodivval
    48. grpodivinv
    49. grpoinvdiv
    50. grpodivf
    51. grpodivcl
    52. grpodivdiv
    53. grpomuldivass
    54. grpodivid
    55. grponpcan
  2. Abelian groups
    1. cablo
    2. df-ablo
    3. isablo
    4. ablogrpo
    5. ablocom
    6. ablo32
    7. ablo4
    8. isabloi
    9. ablomuldiv
    10. ablodivdiv
    11. ablodivdiv4
    12. ablodiv32
    13. ablonncan
    14. ablonnncan1