ONE GROUP
497J, 1998-11-06
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<PAGE>   1

                              BANK ONE CORPORATION
                                        
                             100 East Broad Street
                           Columbus, Ohio 43271-1058

November 6, 1998

Filing Desk
Securities and Exchange Commission
450 Fifth Street, N.W.
Washington, D.C. 20549

Re: The One Group(R) (the "Trust") (File No. 2-95973 and 811-4236); on behalf of
    The One Group(R) U.S. Treasury Securities Money Market Fund, The One
    Group(R) Prime Money Market Fund, The One Group(R) Municipal Money Market
    Fund, The One Group(R) Ohio Municipal Money Market Fund, The One Group(R)
    Treasury Only Money Market Fund, The One Group(R) Income Equity Fund, The
    One Group(R) Disciplined Value Fund, The One Group(R) Growth Opportunities
    Fund, The One Group(R) Equity Index Fund, The One Group(R) Large Company
    Value Fund, The One Group(R) Large Company Growth Fund, The One Group(R)
    Asset Allocation Fund, The One Group(R) Value Growth Fund, The One Group(R)
    Small Capitalization Fund, The One Group(R) International Equity Index Fund,
    The One Group(R) Income Bond Fund, The One Group(R) Ultra Short-Term Income
    Fund, The One Group(R) Limited Volatility Bond Fund, The One Group(R)
    Intermediate Bond Fund, The One Group(R) Government Bond Fund, The One
    Group(R) High Yield Bond Fund, The One Group(R) Treasury & Agency Fund, The
    One Group(R) Municipal Income Fund, The One Group(R) Intermediate Tax-Free
    Bond Fund, The One Group(R) Ohio Municipal Bond Fund, The One Group(R) West
    Virginia Municipal Bond Fund, The One Group(R) Kentucky Municipal Bond Fund,
    The One Group(R) Arizona Municipal Bond Fund, The One Group(R) Louisiana
    Municipal Bond Fund, The One Group(R) Government Money Market Fund, The One
    Group(R) Institutional Prime Money Market Fund, The One Group(R) Investor
    Growth Fund, The One Group(R) Investor Growth and Income Fund, The One
    Group(R) Investor Conservative Growth Fund, and The One Group(R) Investor
    Balanced Fund; Post-Effective Amendment No. 46 to the Registration Statement
    on Form N-1A.


Dear Sir or Madam:


                            RULE 497(J) CERTIFICATION
                            -------------------------  

         Pursuant to the requirements of Rule 497(j) under the Securities Act of
1933, the Registrant certifies that the forms of prospectuses and Statement of
Additional Information that would have been filed under Rule 497(c) would not
have differed from that contained in Post-Effective Amendment No. 46 filed on
October 19, 1998 and effective on November 1, 1998, pursuant to Rule 485(b). The
text of Post-Effective Amendment No. 46 was filed electronically.


                                THE ONE GROUP(R)
                                Registrant



                                /s/ Mark S. Redman
                                ------------------------------------------------
                                Mark S. Redman, President



                                By: /s/ Alan G. Priest
                                    --------------------------------------------
                                    Alan G. Priest, As Attorney-In-Fact
                                    Pursuant to Power of Attorney filed herewith
<PAGE>   2

                                POWER OF ATTORNEY
                                -----------------   


         Mark S. Redman, whose signature appears below, does hereby constitute
and appoint Martin E. Lybecker, Alan G. Priest and Francoise M. Haan, each
individually, his true and lawful attorneys and agents, with power of
substitution or resubstitution, to do any and all acts and things and to execute
any and all instruments which said attorneys and agents, each individually, may
deem necessary or advisable or which may be required to enable The One Group(R)
(the "Trust"), to comply with the Investment Company Act of 1940, as amended,
and the Securities Act of 1933, as amended ("Acts"), and any rules, regulations
or requirements of the Securities and Exchange Commission in respect thereof,
in connection with the filing and effectiveness of the any and all instruments
and/or documents pertaining to the federal registration of the shares of the
Trust, including specifically, but without limiting the generality of the
foregoing, the power and authority to sign in the name and on behalf of the
undersigned as a director and/or officer of the Trust any and all amendments to
the Trust's Registration Statement as filed with the Securities and Exchange
Commission under said Acts, and the undersigned does hereby ratify and confirm
all that said attorneys and agents, or either of them, shall do or cause to be
done by virtue thereof.

Dated: August 23, 1996



                                         /s/ Mark S. Redman
                                         ---------------------------------------
                                         Mark S. Redman


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