In this action for mandamus, we hold that appellee Board of Trustees for the Police Officers Pension Fund (“board”) acted without *551legal authority in approving a pension which the board later rescinded. Thus, the board will not be estopped from reducing pension benefits it had been paying to appellant Reginal Dukes. We, therefore, affirm the trial court’s grant of summary judgment in favor of the board.
Dukes began service with the City of Atlanta Police Department in 1979, and eventually attained the rank of sergeant. Prior to 1979, he had been employed by the DeKalb County Police Department for approximately four years. In 1999 Dukes sought permission from appellee board to receive credit for his prior service with DeKalb County for purposes of calculating his pension benefits. This request was denied by the board on the basis that it was untimely under the Charter of the City of Atlanta and § 6-222 (k) (1) of the 1978 Pension Act.1
In 2001 Dukes again sought permission to receive credit for his DeKalb County service so that he could retire early. In furtherance of that effort, Dukes met with Ray Adams, a senior benefits analyst in the Atlanta Bureau of Employee Benefits. Adams agreed to allow Dukes to purchase credit for his prior DeKalb service in a lump sum at the pay and pension rates in place from 1985 through 1989. Staff in the City’s Bureau of Employee Benefits determined that Dukes could receive credit for his prior service credit at a cost of $20,667.51, and he paid that amount to the Police Officers Pension Fund.
In January 2002, Dukes formally submitted an application to the board for a service pension, requesting a monthly sum of $3,940.87, effective January 1, 2002. He specified in the application that his request was based upon 26.6667 total years of service, “including]... 3.36 prior service.” Dukes’ application was unanimously approved by the board. Dukes retired on December 31, 2001 and began receiving a monthly pension of $3,940.87.
One year later, the board met and rescinded their decision to allow credit for Dukes’ DeKalb County service. Dukes was notified by the board that his receipt of the prior service credit was in “violation of the pension law,” and that his correct monthly pension is $3,338, which resulted in overpayments from January 2002 through December 2002 of $7,576.32. Recognizing that Dukes had purchased his *552DeKalb service credit for $20,667.51, the board deducted the over-payments from the purchase amount and sent Dukes a refund check for the difference of $13,745.23. Instead of negotiating the check, Dukes filed a petition for mandamus to compel the board to reinstate its initial decision and to continue pension benefits in the amount of $3,940.87. The trial court granted summary judgment in favor of the board.2
Dukes urges that his case is controlled in his favor by the estoppel doctrine espoused in Quillian v. Employees’Retirement System of Ga., 259 Ga. 253 (379 SE2d 515) (1989), but although factually very similar, a critical distinguishing factor makes Quillian inapplicable. In Quillian, appellant applied for retirement after having been advised by the Employees Retirement System (“ERS”) that he would accumulate 34 years of creditable service as of a specific date. Appellant received official acknowledgment that his application had been approved and he was informed of the amount of his monthly pension allowance. In reliance on that information, appellant submitted his resignation to the Governor based on 34 years of service with the state. His resignation was accepted, and he began receiving the monthly pension he was promised. Six months later, ERS declared that it had erred in its calculation and it reduced appellant’s pension by almost $1,750 per month. Under those circumstances, the Court ruled that while ERS had the legal authority to determine what pension should be paid, it miscalculated the amount and arrived at an incorrect figure. Consequently, ERS must be estopped from denying the benefits it promised appellant prior to his retirement. In so ruling, the Court made a distinction “between an irregular exercise of a granted power, and the total absence or want of power,” id. at 255 (4) (b), noting that the “public can be and will be estopped by the acts of any public officer done in the exercise of a power which is expressly conferred by law.” (Punctuation omitted; emphasis supplied.) Id. at 254 (3) (a). But the converse is equally true. OCGA § 45-6-5 provides: “Powers of all public officers are defined by law and all persons must take notice thereof. The public may not be estopped by the acts of any officer done in the exercise of an unconferred power.” (Emphasis supplied.) Thus, the question in this case turns on whether Adams *553and the board had the legal authority to disburse retirement benefits based on Dukes’ prior service.
As noted previously, § 6-222 (k) (1) of the 1978 Pension Act authorizes credit for prior service only when two criteria are met: the officer must have completed a minimum of five years of service with the city and must have filed an application with the board five years prior to retirement. Because Dukes did not satisfy the second condition, his entitlement to prior service never vested. Thus, the board’s action in rescinding the credited service was not a recalculation; it was an annulment of an entitlement that had no legal basis. When the pension decision goes to entitlement, as opposed to calculation of benefits, the Quillian estoppel doctrine does not apply. Miller v. Clayton County, 271 Ga. 135 (518 SE2d 402) (1999).
In City of Warner Robins v. Rushing, 259 Ga. 348 (381 SE2d 38) (1989), the Court applied OCGA § 45-6-5 and held that a governing authority may not be estopped regarding an ultra vires act, i.e., where a “government official had no authority to take the action in question.” Id. at 349. See also Black’s Law Dictionary, Sixth ed. 1990, p. 1522 (an act is ultra vires if it is “performed without any authority to act on [the] subject”).
The dissent asserts that the board’s action in awarding credit for Dukes’ DeKalb County service was not an ultra vires act, and that in approving the initial pension, the board acted within its granted powers. But the dissent utterly fails to consider the limitations placed on the board pursuant to the mandatory language of § 6-222 (k) (1). If the requirements of that ordinance were not satisfied, Dukes was absolutely “[in]eligible for such prior service credit.” Although the dissent refers to the board’s actions as an “exercise of a granted power,” and points to § 6-222 (d) of the City’s 1978 Pension Act to confer this authority, that provision states only that an employee with 15 years of active service “may as a matter of right retire from active service and receive an early retirement benefit.” It does not confer upon the board the authority to disregard or deviate from the mandatory language of § 6-222 (k) (1). Indeed, there is no such authority.3
We appreciate that the result in this case appears harsh in light of the fact that Dukes relied on the board’s approval of his pension application in deciding to retire; however, “[detrimental reliance, which is a necessary element of any claim of equitable estoppel... is not a factor where estoppel cannot be applied against the city as a matter of law.” City of Warner Robins, supra at 348-349. See also *554Miller v. Clayton County, supra.4 *Here Dukes’ entitlement to the prior service credit never vested; thus, the board lacked any “power which is expressly conferred by law” to award a pension based on that prior service. Accordingly, Dukes may not avail himself of the doctrine of estoppel and the trial court properly granted summary judgment in favor of the board.
Judgment affirmed.
All the Justices concur, except Sears, C. J., Hunstein, P. J., and Carley, J., who dissent.Under the 1978 Pension Act, an officer or employee is entitled to all of the forms and types of prior service authorized, but “[t]o be eligible for such prior service credit, the officer or employee must have completed at least five (5) continuous years in the employment of the city, and must have filed, five years prior thereto, an application with the board of trustees for such prior service credit.” § 6-222 (k) (1). Although Dukes had satisfied the continuous service requirement, the board determined that he had not applied for prior service credit within the time allotted by § 6-222 (k) (1).
Ordinarily, Dukes would have been required to seek review of an adverse ruling by the board ‘Toy writ of certiorari in the superior court.” Atlanta City Ordinance § 6-285. But in this case, as the trial court correctly ruled, Dukes was precluded from pursuing that remedy because the board did not notify him of its decision until the time for filing a petition for certiorari had expired. Thus, mandamus was the only available remedy. Compare DeKalb County v. Wal-Mart Stores, 278 Ga. 501 (604 SE2d 162) (2004). And since there was no administrative decision to review, Dukes was entitled to a direct appeal from the denial of his petition for mandamus. See Ferguson v. Composite State Bd. of Medical Examiners, 275 Ga. 255 (564 SE2d 715) (2002).
The dissent acknowledges that “[t]he Board may not be authorized to waive the five-year procedural requirement for applying for recognition of prior service.”
Under facts very similar to ours, the Supreme Court of Oklahoma recently held that incorrect information given to a police officer by the board as to when benefits would begin, did not estop the board from relying on a statutory prohibition against paying benefits. Strong v. Ok. Police Pension &c. Bd.., 115 P3d 889 (2005). In so ruling, the Court surveyed a majority of other jurisdictions which “determinfed] that erroneous information given to a claimant could not estop the government from denying benefits not otherwise permitted by law.” Id., 115 P3d 889, 895, n. 23.